Fluctuating nonlinear hydrodynamics of flocking
Yadav, Sunil Kumar; Das, Shankar P.
2018-03-01
Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.
Hydrodynamic stability and stellar oscillations
Indian Academy of Sciences (India)
Chandrasekhar's monograph on Hydrodynamic and hydromagnetic stability, published in 1961, is a standard ... the Astrophysics Data System shows about 2500 citations to this monograph and what is remarkable is that ... form the bulk of the book are devoted to convection, or the thermal instability of a layer of fluid heated ...
Hydrodynamic and hydromagnetic stability
Chandrasekhar, S
1981-01-01
Dr. Chandrasekhar's book received high praise when it first appeared in 1961 as part of Oxford University Press' International Series of Monographs on Physics. Since then it has been reprinted numerous times in its expensive hardcover format. This first lower-priced, sturdy paperback edition will be welcomed by graduate physics students and scientists familiar with Dr. Chandrasekhar's work, particularly in light of the resurgence of interest in the Rayleigh-Bénard problem. This book presents a most lucid introduction to the Rayleigh-Bénard problem: it has also been applauded for its thorough, clear coverage of the theory of instabilities causing convection. Dr. Chandrasekhar considers most of the typical problems in hydromagnetic stability, with the exception of viscous shear flow; a specialized domain deserving a book unto itself. Contents include: Rotation; Stability of More General Flows; Bénard Problem; Gravitational Equilibrium and Instability; Stability of a Magnetic Field; Thermal Instability of a L...
On the nonlinear stability of dissipative fluids
International Nuclear Information System (INIS)
Tasso, H.; Camargo, S.J.
1991-02-01
A general sufficient condition for nonlinear stability of steady and unsteady flows in hydrodynamics and magnetohydrodynamics is derived. It leads to strong limitations in the Reynolds and magnetic Reynolds numbers. It is applied to the stability of generalized time-dependent planar Couette flows in magnetohydrodynamics. Reynolds and magnetic Reynolds numbers have to be typically less than 2π 2 for stability. (orig.)
Linear and nonlinear stability in resistive magnetohydrodynamics
International Nuclear Information System (INIS)
Tasso, H.
1994-01-01
A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its open-quotes nearnessclose quotes to necessity is analysed. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with open-quotes unconditionalclose quotes stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed. 23 refs
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Nonlinear stability of supersonic jets
Tiwari, S. N. (Principal Investigator); Bhat, T. R. S. (Principal Investigator)
1996-01-01
The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.
Stabilizing geometry for hydrodynamic rotary seals
Dietle, Lannie L.; Schroeder, John E.
2010-08-10
A hydrodynamic sealing assembly including a first component having first and second walls and a peripheral wall defining a seal groove, a second component having a rotatable surface relative to said first component, and a hydrodynamic seal comprising a seal body of generally ring-shaped configuration having a circumference. The seal body includes hydrodynamic and static sealing lips each having a cross-sectional area that substantially vary in time with each other about the circumference. In an uninstalled condition, the seal body has a length defined between first and second seal body ends which varies in time with the hydrodynamic sealing lip cross-sectional area. The first and second ends generally face the first and second walls, respectively. In the uninstalled condition, the first end is angulated relative to the first wall and the second end is angulated relative to the second wall. The seal body has a twist-limiting surface adjacent the static sealing lip. In the uninstalled condition, the twist-limiting surface is angulated relative to the peripheral wall and varies along the circumference. A seal body discontinuity and a first component discontinuity mate to prevent rotation of the seal body relative to the first component.
Control design of a nonlinear controller to stabilize the nonlinear ...
African Journals Online (AJOL)
This article presents the design of a highly efficient nonlinear0 controller which is a kind of an Active Queue Management (AQM) scheme to stabilize the nonlinear TCP model dynamics. Specific boundary conditions have been considered for stability occurrences and have been compared with other existing Active Queue ...
Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings
Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis
2014-05-01
The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps.
Zhang, Geng; Sun, Di-Hua; Liu, Hui; Chen, Dong
2017-11-01
In this paper, a new lattice hydrodynamic model with consideration of the density difference of a lattice's current density and its anticipative density is proposed. The influence of lattice's self-anticipative density on traffic stability is revealed through linear stability theory and it shows that lattice's self-anticipative density can improve the stability of traffic flow. To describe the phase transition of traffic flow, the mKdV equation near the critical point is derived by using nonlinear analysis method. The propagating behavior of density wave in the unstable region can be described by the kink-antikink soliton of the mKdV equation. Numerical simulation validates the analytical results, which shows that traffic jam can be suppressed efficiently by considering lattice's self-anticipative density in the modified lattice hydrodynamic model.
Methods of stability analysis in nonlinear mechanics
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs
Yeo, Joonhyun
2009-11-01
We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.
On Stabilization of Nonautonomous Nonlinear Systems
International Nuclear Information System (INIS)
Bogdanov, A. Yu.
2008-01-01
The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.
Sun, Di-Hua; Zhang, Geng; Zhao, Min; Cheng, Sen-Lin; Cao, Jian-Dong
2018-03-01
Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink-antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.
Nonlinear stability of ideal fluid equilibria
International Nuclear Information System (INIS)
Holm, D.D.
1988-01-01
The Lyapunov method for establishing stability is related to well- known energy principles for nondissipative dynamical systems. A development of the Lyapunov method for Hamiltonian systems due to Arnold establishes sufficient conditions for Lyapunov stability by using the energy plus other conserved quantities, together with second variations and convexity estimates. When treating the stability of ideal fluid dynamics within the Hamiltonian framework, a useful class of these conserved quantities consists of the Casimir functionals, which Poisson-commute with all functionals of the dynamical fluid variables. Such conserved quantities, when added to the energy, help to provide convexity estimates that bound the growth of perturbations. These convexity estimates, in turn, provide norms necessary for establishing Lyapunov stability under the nonlinear evolution. In contrast, the commonly used second variation or spectral stability arguments only prove linearized stability. As ideal fluid examples, in these lectures we discuss planar barotropic compressible fluid dynamics, the three-dimensional hydrostatic Boussinesq model, and a new set of shallow water equations with nonlinear dispersion due to Basdenkov, Morosov, and Pogutse[1985]. Remarkably, all three of these samples have the same Hamiltonian structure and, thus, possess the same Casimir functionals upon which their stability analyses are based. We also treat stability of modified quasigeostrophic flow, a problem whose Hamiltonian structure and Casimirs closely resemble Arnold's original example. Finally, we discuss some aspects of conditional stability and the applicability of Arnold's development of the Lyapunov technique. 100 refs
Structural stability of nonlinear population dynamics
Cenci, Simone; Saavedra, Serguei
2018-01-01
In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.
Saturation and stability of nonlinear photonic crystals
International Nuclear Information System (INIS)
Franco-Ortiz, M; Corella-Madueño, A; Rosas-Burgos, R A; Adrian Reyes, J; Avendaño, Carlos G
2017-01-01
We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions. (paper)
Nonlinear hydrodynamics from flow of retarded Green's function
Banerjee, N.; Dutta, S.
2010-01-01
We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-current of dual gauge theory in presence of generic higher derivative terms in bulk Lagrangian. These are first order non-linear Riccati equations. We solve these flow equations analytically and obtain second
Nonlinear stability of a brane wormhole
Akai, Yumi; Nakao, Ken-ichi
2017-07-01
We analytically study the nonlinear stability of a spherically symmetric wormhole supported by an infinitesimally thin brane of negative tension, which has been devised by Barcelo and Visser. We consider a situation in which a thin spherical shell composed of dust falls into an initially static wormhole; the dust shell plays the role of the nonlinear disturbance. The self-gravity of the falling dust shell is completely taken into account through Israel's formalism of the metric junction. When the dust shell goes through the wormhole, it necessarily collides with the brane supporting the wormhole. We assume the interaction between these shells is only gravity and show the condition under which the wormhole stably persists after the dust shell goes through it.
Beam stability ampersand nonlinear dynamics. Formal report
International Nuclear Information System (INIS)
Parsa, Z.
1996-01-01
This report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors
International Nuclear Information System (INIS)
Elliott, T S; Majdalani, J
2014-01-01
Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Integrability and Linear Stability of Nonlinear Waves
Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo
2018-03-01
It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Directory of Open Access Journals (Sweden)
Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
AQM) scheme employing .... A nonlinear control design is considered for application in this case, so that when there is any change in network .... shows that the system is asymptotically stable with a negative definite solution in equation (14).
Nonlinear stability control and λ-bifurcation
International Nuclear Information System (INIS)
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Hydrodynamic theory of convective transport across a dynamically stabilized diffuse boundary layer
International Nuclear Information System (INIS)
Gerhauser, H.
1983-09-01
The diffuse boundary layer between miscible liquids is subject to Rayleigh-Taylor instabilities if the heavy fluid is supported by the light one. The resulting rapid interchange of the liquids can be suppressed by enforcing vertical oscillations on the whole system. This dynamic stabilization is incomplete and produces some peculiar novel transport phenomena such as decay off the density profile into several steps, periodic peeling of density sheets of the boundary layer and the appearance of steady vortex flow. The theory presented in this paper identifies the basic mechanism as formation of convective cells leading to enhanced diffusion, and explains previous experimental results with water and ZnJ 2 -solutions. A nonlinear treatment of the stationary convective flow problem gives the saturation amplitude of the ground mode and provides an upper bound for the maximum convective transport. The hydrodynamic model can be used for visualizing similar transport processes in the plasma of toroidal confinement devices such as sawtooth oscillations in soft disruptions of tokamak discharges and anomalous diffusion by excitation of convective cells. The latter process is investigated here in some detail, leading to the result that the maximum possible transport is of the order of Bohm diffusion. (orig.)
Directory of Open Access Journals (Sweden)
Muhammad Yasar Javaid
2017-07-01
Full Text Available We are developing a prototype underwater glider for subsea payload delivery. The idea is to use a glider to deliver payloads for subsea installations. In this type of application, the hydrodynamic forces and dynamic stability of the glider is of particular importance, as it has implications on the glider's endurance and operation. In this work, the effect of two different wing forms, rectangular and tapered, on the hydrodynamic characteristics and dynamic stability of the glider were investigated, to determine the optimal wing form. To determine the hydrodynamic characteristics, tow tank resistance tests were carried out using a model fitted alternately with a rectangular wing and tapered wing. Steady-state CFD analysis was conducted using the hydrodynamic coefficients obtained from the tests, to obtain the lift, drag and hydrodynamic derivatives at different angular velocities. The results show that the rectangular wing provides larger lift forces but with a reduced stability envelope. Conversely, the tapered wing exhibits lower lift force but improved dynamic stability.
Shiau, Ting N.; Hwang, Jon L.; Chang, Yuan B.
1992-06-01
The stability of steady state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations which govern the motion of rotor bearing system are obtained by using the Generalized Polynomial Expansion Method. The steady state response of system is obtained by using the hybrid numerical method which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.
Rippled shock front solutions for testing hydrodynamic stability simulations
International Nuclear Information System (INIS)
Munro, D.H.
1989-01-01
The response of a shock front to arbitrary small perturbations can be calculated analytically. Such rippled shock front solutions are useful for determining the accuracy of hydrodynamic simulation codes such as LASNEX [Comments Plasma Phys. Controlled Fusion 2, 51 (1977)], which are used to compute perturbation growth in inertial fusion targets. The LASNEX fractional errors are of order κ 2 L 2 , where κ is the transverse wavenumber of the perturbation, and L is the largest zone dimension. Numerical errors are about 25% for a calculation using 26 zones per transverse wavelength
Stabilization of nonlinear excitations by disorder
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem...
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
Energy Technology Data Exchange (ETDEWEB)
Mikaelian, K O
2009-09-28
We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.
Uniform stability of damped nonlinear vibrations of an elastic string
Indian Academy of Sciences (India)
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is ...
New stability conditions for nonlinear time varying delay systems
Elmadssia, S.; Saadaoui, K.; Benrejeb, M.
2016-07-01
In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum
McMillan, Edwin M.
1968-03-29
Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
Advanced nonlinear stability analysis of boiling water nuclear reactors
Lange, Carsten
2009-01-01
This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in whi...
Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control
Nguyen, Nhan T.; Boskovic, Jovan D.
2008-01-01
This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.
International Nuclear Information System (INIS)
Hunter, J.H.
1986-01-01
This report addresses two broad aspects of the behaviors of hydrodynamic flows, resulting from laser heated, exploding foils. In Part I, various aspects of the similarity solutions are considered, whereas in Part II the stability of the flows at early times are examined, before the similarity solutions are established. 5 refs., 3 figs
Sharp nonlinear stability for centrifugal filtration convection in magnetizable media.
Saravanan, S; Brindha, D
2011-11-01
A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection.
Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
is used to formularize the delay differential equation in equation. (13), which accounts for the delayed terms in the system. By applying the Leibniz integration rule, the derivative. •. V shows that the system is asymptotically stable with a negative definite solution in equation (14). The conditions for the stability are: •. The delay ...
Linear and nonlinear stability analysis, associated to experimental fast reactors
International Nuclear Information System (INIS)
Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.
1980-07-01
Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt
Analysis of the hydrodynamic stability of natural circulation
International Nuclear Information System (INIS)
Olive, J.; Baby, J.P.
1980-01-01
A mathematical model (EOLE) for the analysis of the stability of boilers with natural circulation is discussed. The method employed consists in linearizing one-dimensional flow equations and in integrating them while employing the Laplace transformation. The properties of a two-phase fluid are schematized by a homogeneous model with slip. The computation results in the circulation loop transfer functions and its natural modes of oscillation (frequency and damping). A discussion follows which compares results obtained with this method to those of other existing models in the case of a straight pipe with forced circulation. Agreement proved to be satisfactory. The results are then given of a parametric study involving the stability of a PWR natural circulation steam generator. These results show that the model can satisfy, at least qualitatively, trends observed empirically or obtained with other more complex theoretical models. (author)
Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Delchini, Marc O., E-mail: delchinm@email.tamu.edu; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim, E-mail: jim.morel@tamu.edu
2015-09-01
The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The method of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.
Robust stabilization of nonlinear systems: The LMI approach
Directory of Open Access Journals (Sweden)
iljak D. D.
2000-01-01
Full Text Available This paper presents a new approach to robust quadratic stabilization of nonlinear systems within the framework of Linear Matrix Inequalities (LMI. The systems are composed of a linear constant part perturbed by an additive nonlinearity which depends discontinuously on both time and state. The only information about the nonlinearity is that it satisfies a quadratic constraint. Our major objective is to show how linear constant feedback laws can be formulated to stabilize this type of systems and, at the same time, maximize the bounds on the nonlinearity which the system can tolerate without going unstable. We shall broaden the new setting to include design of decentralized control laws for robust stabilization of interconnected systems. Again, the LMI methods will be used to maximize the class of uncertain interconnections which leave the overall system connectively stable. It is useful to learn that the proposed LMI formulation “recognizes” the matching conditions by returning a feedback gain matrix for any prescribed bound on the interconnection terms. More importantly, the new formulation provides a suitable setting for robust stabilization of nonlinear systems where the nonlinear perturbations satisfy the generalized matching conditions.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M.; Hallo, L. [Bordeaux-1 Univ., CELIA UMR 5107, 33 - Talence (France)
2006-06-15
This study deals with the hydrodynamic stability of a planar target in the context of inertial confinement fusion direct drive. Recently, different schemes have been proposed in order to reduce ablative Rayleigh-Taylor growth. They are based on the target adiabatic shaping in the ablation zone. In this work, we consider an adiabatic shaping scheme by relaxation: a prepulse is followed by a relaxation period where the laser is turned off. A numerical study is performed with a perturbation code dedicated to the linear stability analysis. The simulations show stabilizing effects of the relaxation scheme on the linear Rayleigh-Taylor growth rate. Influence of the picket parameters is also discussed. (authors)
Influence of hydrodynamic thrust bearings on the nonlinear oscillations of high-speed rotors
Chatzisavvas, Ioannis; Boyaci, Aydin; Koutsovasilis, Panagiotis; Schweizer, Bernhard
2016-10-01
This paper investigates the effect of hydrodynamic thrust bearings on the nonlinear vibrations and the bifurcations occurring in rotor/bearing systems. In order to examine the influence of thrust bearings, run-up simulations may be carried out. To be able to perform such run-up calculations, a computationally efficient thrust bearing model is mandatory. Direct discretization of the Reynolds equation for thrust bearings by means of a Finite Element or Finite Difference approach entails rather large simulation times, since in every time-integration step a discretized model of the Reynolds equation has to be solved simultaneously with the rotor model. Implementation of such a coupled rotor/bearing model may be accomplished by a co-simulation approach. Such an approach prevents, however, a thorough analysis of the rotor/bearing system based on extensive parameter studies. A major point of this work is the derivation of a very time-efficient but rather precise model for transient simulations of rotors with hydrodynamic thrust bearings. The presented model makes use of a global Galerkin approach, where the pressure field is approximated by global trial functions. For the considered problem, an analytical evaluation of the relevant integrals is possible. As a consequence, the system of equations of the discretized bearing model is obtained symbolically. In combination with a proper decomposition of the governing system matrix, a numerically efficient implementation can be achieved. Using run-up simulations with the proposed model, the effect of thrust bearings on the bifurcations points as well as on the amplitudes and frequencies of the subsynchronous rotor oscillations is investigated. Especially, the influence of the magnitude of the axial force, the geometry of the thrust bearing and the oil parameters is examined. It is shown that the thrust bearing exerts a large influence on the nonlinear rotor oscillations, especially to those related with the conical mode of the
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.
Passivity Based Stabilization of Non-minimum Phase Nonlinear Systems
Czech Academy of Sciences Publication Activity Database
Travieso-Torres, J.C.; Duarte-Mermoud, M.A.; Zagalak, Petr
2009-01-01
Roč. 45, č. 3 (2009), s. 417-426 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear systems * stabilisation * passivity * state feedback Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-passivity based stabilization of non-minimum phase nonlinear systems.pdf
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Hydrodynamic Fluid Film Bearings and Their Effect on the Stability of Rotating Machinery
2006-11-01
Refer to [2] for details on the analytical solution of Eqn. (18). This is not the case for squeeze film dampers (SFDs), however, since the long...on Finite Length Sealed Squeeze Film Dampers , L. San Andrés & J.M. Vance, ASLE Transactions, 30, 3, pp. 384-393, 1987. [5] Turbomachinery...RTO-EN-AVT-143 10 - 1 Hydrodynamic Fluid Film Bearings and Their Effect on the Stability of Rotating Machinery Luis San Andrés Mast
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, B.A.
1987-01-01
Four levels of nonlinear hydrodynamic description are presented for a nondissipative multicondensate solution of superfluids with vorticity. First, the multivelocity superfluid (MVSF) theory is extended to the case of a multivelocity superfluid plasma (MVSP), in which some of the superfluid condensates (protons, say) are charged and coupled electromagnetically to an additional, normal, charged fluid (electrons). The resulting drag-current density is derived due to the electromagnetic coupling of the condensates with the normal fluids. For the case of one charged condensate, the MVSP equations simplify to what we call superfluid Hall magnetohydrodynamics (SHMHD) in the approximation that displacement current and electron inertia are negligible, and local charge neutrality is imposed. The contribution of the charged condensate to the Hall drift force is determined. In turn, neglecting the Hall effect in SHMHD gives the equations of superfluid magnetohydrodynamics (SMHD). Each set of equations (MVSF, MVSP, SHMHD, and SMHD) is shown to be Hamiltonian and to possess a Poisson bracket associated with the dual space of a corresponding semidirect-product Lie algebra with a generalized two-cocycle defined on it. Topological conservation laws (helicities) associated with the kernels of these Lie algebras are also discussed as well as those associated physically with generalized Kelvin theorems for conservation of superfluid circulation around closed loops moving with the normal fluid
On the hydrodynamics of a solvent-satured lipid bilayer. 2. Stability criteria
International Nuclear Information System (INIS)
Bisch, P.M.; Wendel, H.
1983-01-01
The semiphenomenological model introduced recently is used to investigate the role of steric forces on the dynamics of black lipid films. A linear stability analysis of hydrodynamic fluctuations for lipid films submitted to an applyed electric field is performed. By neglecting dissipation, this our analysis is concentrated on the competitive effects of electrostatic, van der Waals and steric forces. In the long wavelenght limit it is shown that the stability of the film against bending deformations is governed by the total film tension. Similarly, for periodic thickness fluctuations the stability is determined by the film elasticity. In both cases a stabilizing positive contribution is found of steric forces produced by the overlap of lipid chains at the center of the film. The stability diagram shows a region, for sufficiently small thickness, where only bending modes are unstable. (Author) [pt
Directory of Open Access Journals (Sweden)
Ahmed Syed Uzair
2012-09-01
Full Text Available Hydrodynamic analysis of a surface-piercing body with an open chamber was performed with incident regular waves and forced-heaving body motions. The floating body was simulated in the time domain using a 2D fully nonlinear numerical wave tank (NWT technique based on potential theory. This paper focuses on the hydrodynamic behavior of the free surfaces inside the chamber for various input conditions, including a two-input system: both incident wave profiles and forced body velocities were implemented in order to calculate the maximum surface elevations for the respective inputs and evaluate their interactions. An appropriate equivalent linear or quadratic viscous damping coefficient, which was selected from experimental data, was employed on the free surface boundary inside the chamber to account for the viscous energy loss on the system. Then a comprehensive parametric study was performed to investigate the nonlinear behavior of the wave-body interaction.
Barrett, L. E.; Gunter, E. J.
1980-01-01
A method of analyzing the first mode stability and unbalance response of multimass flexible rotors is presented whereby the multimass system is modeled as an equivalent single mass modal model including the effects of rotor flexibility, general linearized hydrodynamic journal bearings, squeeze film bearing supports and rotor aerodynamic cross coupling. Expressions for optimum bearing and support damping are presented for both stability and unbalance response. The method is intended to be used as a preliminary design tool to quickly ascertain the effects of bearing and support changes on rotor-bearing system performance.
Deciphering the imprint of topology on nonlinear dynamical network stability
International Nuclear Information System (INIS)
Nitzbon, J; Schultz, P; Heitzig, J; Kurths, J; Hellmann, F
2017-01-01
Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields. (paper)
Stability of non-linear constitutive formulations for viscoelastic fluids
Siginer, Dennis A
2014-01-01
Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.
The Local Stability of Solutions for a Nonlinear Equation
Directory of Open Access Journals (Sweden)
Haibo Yan
2014-01-01
Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.
Robust stabilization of nonlinear systems by quantized and ternary control
Persis, Claudio De
2009-01-01
Results on the problem of stabilizing a nonlinear continuous-time minimum-phase system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the stability problem of a class of nonlinear switched systems with partitioned state-space and state-dependent switching. In lieu of the Caratheodory solutions, the general Filippov solutions are considered. This encapsulates solutions with infinite switching in finite time....... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
Nonlinear stability analysis of the frame structures
Directory of Open Access Journals (Sweden)
Ćorić Stanko
2016-01-01
Full Text Available In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this analysis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this analysis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was also established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3 and national (JUS standards for the steel structures. By the given procedure in this paper it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain.
International Nuclear Information System (INIS)
Alvarez R, J.T.
1998-01-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix
Stabilization Approaches for Linear and Nonlinear Reduced Order Models
Rezaian, Elnaz; Wei, Mingjun
2017-11-01
It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.
Stabilization of switched nonlinear systems with unstable modes
Yang, Hao; Cocquempot, Vincent
2014-01-01
This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...
Nonlinear stability and time step selection for the MPM method
Berzins, Martin
2018-01-01
The Material Point Method (MPM) has been developed from the Particle in Cell (PIC) method over the last 25 years and has proved its worth in solving many challenging problems involving large deformations. Nevertheless there are many open questions regarding the theoretical properties of MPM. For example in while Fourier methods, as applied to PIC may provide useful insight, the non-linear nature of MPM makes it necessary to use a full non-linear stability analysis to determine a stable time step for MPM. In order to begin to address this the stability analysis of Spigler and Vianello is adapted to MPM and used to derive a stable time step bound for a model problem. This bound is contrasted against traditional Speed of sound and CFL bounds and shown to be a realistic stability bound for a model problem.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Stability of nonlinear ion sound waves and solitons in plasmas
International Nuclear Information System (INIS)
Infeld, E.; Rowlands, G.
1979-01-01
Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the Korteweg-de Vries equation, which gives stability for non linear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5 A three-dimensional generalization of the Korteweg-de Vries equation is considered but this leads to stability for all non linear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit. (author)
Improved algorithm for solving nonlinear parabolized stability equations
International Nuclear Information System (INIS)
Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng
2016-01-01
Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)
Improved algorithm for solving nonlinear parabolized stability equations
Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng
2016-08-01
Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).
Asymptotic stabilization of nonlinear systems using state feedback
International Nuclear Information System (INIS)
D'Attellis, Carlos
1990-01-01
This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es
Linear and nonlinear kinetic-stability studies in tokamaks
International Nuclear Information System (INIS)
Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.
1982-09-01
This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities
On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability
Janke, Erik; Balakumar, Ponnampalam
1999-01-01
The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.
Nonlinear and Non-ideal Effects on FRC Stability
International Nuclear Information System (INIS)
Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.
2002-01-01
New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs in strongly kinetic and small-gyroradius, MHD-like regimes. The n = 1 tilt instability mechanism and stabilizing factors are investigated in detail including nonlinear and resonant particle effects, particle losses along the open field lines, and Hall stabilization. It is shown that the Hall effect determines the mode rotation and change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to the finite Larmor radius effects. Resonant particle effects are important in the large gyroradius regime regardless of the separatrix shape, and even in cases when a large fraction of the particle orbits are stochastic. Particle loss along the open field lines has a destabilizing effect on the tilt mode and contributes to the ion spin up in toroidal direction. The nonlinear evolution of unstable modes in both kinetic and small-gyroradius FRCs is shown to be considerably slower than that in MHD simulations. Our simulation results demonstrate that a combination of kinetic and nonlinear effects is a key for understanding the experimentally observed FRC stability properties
International Nuclear Information System (INIS)
Jammazi, Chaker
2009-01-01
The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.
Surf Zone Hydrodynamics and its Utilization in Biotechnical Stabilization of Water Reservoir Banks
Directory of Open Access Journals (Sweden)
Petr Pelikán
2014-01-01
Full Text Available The water reservoir banks are eroded mainly by two factors. The first one is wave action (i.e. wave abrasion affecting the bank in direction from the reservoir. The second one is the influence of water flowing downward over the bank surface in direction from land into the reservoir (e.g. rainfall. The determination of regular altitudinal emplacement of proper designed particular biotechnical stabilization elements is the most important factor on which the right functionality of whole construction depends. Surf zone hydrodynamics solves the wave and water level changes inside the region extending from the wave breaking point to the limit of wave up-rush. The paper is focused on the utilization of piece of knowledge from a part of sea coast hydrodynamics and new approach in its application in the conditions of inland water bodies when designing the biotechnical stabilization elements along the shorelines. The “reinforced grass carpets” as a type of biotechnical method of bank stabilization are presented in the paper; whether the growth of grass root system is dependent on presence or absence of geomats in the soil structure and proceeding of their establishment on the shorelines.
Hydrodynamic stability theory of double ablation front structures in inertial confinement fusion
International Nuclear Information System (INIS)
Yanez Vico, C.
2012-11-01
For moderate-Z materials, the hydrodynamic structure of the ablation region formed by the irradiation of high intensity laser beams differs from that of low-Z materials (hydrogenic ablators). In particular, the role played by the radiative energy flux becomes non-negligible for increasing atomic number material and ended up forming a second ablation front. This structure of two separated ablation fronts, called double ablation (DA) front, was confirmed in the simulations carried out by Fujioka et al. In this work a linear stability theory of DA fronts is developed for direct-drive inertial confinement fusion targets. Two models are proposed. First, a sharp boundary model where the thin front approximation is assumed for both ablation fronts. The information about the corona region that permits to close the sharp boundary model is obtained from a prior self-consistent analysis of the electronic-radiative ablation (ERA) front. Numerical results are presented as well as an analytical approach for the radiation dominated regime of very steep double ablation front structure. Second, a self-consistent numerical method where the finite length of the ablation fronts is considered. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using one-dimensional simulation results. Numerical dispersion relation is compared to the analytical sharp boundary model showing an excellent agreement for the radiation dominated regime, and the stabilization due to smooth profiles. 2D simulations are presented to validate the linear stability theory
Camporeale, Carlo; Ridolfi, Luca
2012-06-08
A novel hydrodynamic-driven stability analysis is presented for surface patterns on speleothems, i.e., secondary sedimentary cave deposits, by coupling fluid dynamics to the geochemistry of calcite precipitation or dissolution. Falling film theory provides the solution for the flow-field and depth perturbations, the latter being crucial to triggering patterns known as crenulations. In a wide range of Reynolds numbers, the model provides the dominant wavelengths and pattern celerities, in fair agreement with field data. The analysis of the phase velocity of ridges on speleothems has a potential as a proxy of past film flow rates, thus suggesting a new support for paleoclimate analyses.
Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient
Directory of Open Access Journals (Sweden)
Zaiyue Yang
2014-01-01
Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.
pth Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations
Directory of Open Access Journals (Sweden)
Xuetao Yang
2014-01-01
Full Text Available We are concerned with the exponential stability problem of a class of nonlinear hybrid stochastic heat equations (known as stochastic heat equations with Markovian switching in an infinite state space. The fixed point theory is utilized to discuss the existence, uniqueness, and pth moment exponential stability of the mild solution. Moreover, we also acquire the Lyapunov exponents by combining the fixed point theory and the Gronwall inequality. At last, two examples are provided to verify the effectiveness of our obtained results.
Stability, Nonlinearity and Reliability of Electrostatically Actuated MEMS Devices
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Di Chen
2007-05-01
Full Text Available Electrostatic micro-electro-mechanical system (MEMS is a special branch with a wide range of applications in sensing and actuating devices in MEMS. This paper provides a survey and analysis of the electrostatic force of importance in MEMS, its physical model, scaling effect, stability, nonlinearity and reliability in detail. It is necessary to understand the effects of electrostatic forces in MEMS and then many phenomena of practical importance, such as pull-in instability and the effects of effective stiffness, dielectric charging, stress gradient, temperature on the pull-in voltage, nonlinear dynamic effects and reliability due to electrostatic forces occurred in MEMS can be explained scientifically, and consequently the great potential of MEMS technology could be explored effectively and utilized optimally. A simplified parallel-plate capacitor model is proposed to investigate the resonance response, inherent nonlinearity, stiffness softened effect and coupled nonlinear effect of the typical electrostatically actuated MEMS devices. Many failure modes and mechanisms and various methods and techniques, including materials selection, reasonable design and extending the controllable travel range used to analyze and reduce the failures are discussed in the electrostatically actuated MEMS devices. Numerical simulations and discussions indicate that the effects of instability, nonlinear characteristics and reliability subjected to electrostatic forces cannot be ignored and are in need of further investigation.
Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion
Shabana, Ahmed A.; Zaher, Mohamed H.; Recuero, Antonio M.; Rathod, Cheta
2011-11-01
General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of
Stability of nonlinear repetitive processes with possible failures
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J. P. Emelianova
2014-01-01
Full Text Available Nonlinear discrete-time repetitive processes with Markovian jumps are considered. For such processes stability analysis is developed and this result is then applied to iterative learning control design.Stability of nonlinear repetitive processes has not been developed previously in the current literature. This paper proposes and characterizes a stability theory for nonlinear repetitive processes that includes stability along the pass of linear examples as a special case.For considered systems the second Lyapunov method cannot be used. Because repetitive processes belong to a class of 2D systems in which state variables are depend on two independent variables and cannot be solved using all first differences of state variables. It is not allow us to find a first difference of Lyapunov function along the trajectory of the system without finding solution of a system of equations that fully excludes a main advantage of second Lyapunov method. At the same time the use of vector Lyapunov functions and discrete-time counterpart of the divergence operator of this function along the trajectories of system instead of first difference allow us to obtain constructive results.In this paper based on vector Lyapunov function approach sufficient conditions for pass profile exponential stability are obtained which in the linear case are obtained in terms of linear matrix inequalities and in the linear case without failures these conditions are reduced to known conditions of stability along the passA major application area where repetitive process stability theory can be used is Iterative Learning Control (ILC. The idea of ILC is following.If the system repeats the same finite duration operation over and over again, it is reasonable to use the input and output variables on the current pass for improving accuracy of performance of operations on the next pass.The new theoretical stability results are applied to ILC design under possible information failures. The ILC
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
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Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Surpassing the energy method for nonlinear fluid stability
Goluskin, David; Fuentes, Federico
2017-11-01
A basic question in fluid stability is whether a laminar flow is nonlinearly stable to all perturbations. The typical way to verify stability, called the energy method, is to show that the energy of a perturbation must decay monotonically. The energy method is known to be overly conservative in many systems, particularly when turbulence arises subcritically, such as in parallel shear flows. The energy method is a special case of a Lyapunov function method in which the Lyapunov function is the perturbation energy. This talk will present a more general approach in which the Lyapunov functions (1) are not restricted to being quadratic but instead are higher-degree polynomials, and (2) can depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal construction of such Lyapunov functions is complicated but can be done with computer assistance by formulating a polynomial optimization problem, which in turn is formulated as a semidefinite program. This talk will describe the general framework of the method. A companion talk by Federico Fuentes will illustrate its application to planar Couette flow, where we have verified nonlinear stability at larger Reynolds numbers than is possible using the energy method.
Coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers.
Zhang, Junshi; Chen, Hualing; Li, Bo; McCoul, David; Pei, Qibing
2015-10-14
This article describes the development of an analytical model to study the coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers (DEs) under non-equibiaxial tensile forces by utilizing the method of virtual work. Numerically calculated results are employed to predict this nonlinear dynamic behavior. The resonant frequency (where the amplitude-frequency response curve peaks) and the amplitude-frequency response of the deformation in both in-plane directions are tuned by varying the values of tensile force. The oscillation response in the two in-plane directions exhibits strong nonlinearity and coupling with each other, and is tuned by the changing tensile forces under a specific excitation frequency. By varying the values of tensile forces, the dynamic viscoelastic creep in a certain in-plane direction can be eliminated. Phase diagrams and Poincaré maps under several values of tensile forces are utilized to study the stability evolution of the DE system under non-equibiaxial tensile forces.
Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
Emerson, Benjamin; Lieuwen, Tim
2017-11-01
This study investigates the forced response characteristics of axisymmetric structures in density-stratified swirling jets. The reacting, swirling jet is an important canonical flow field for modern combustion systems. This work is motivated by the combustion instability problem for such systems, where acoustically excited vortical structures may drive oscillatory heat release of combustion. Previous hydrodynamics studies have shown that the stability of helical structures is highly sensitive to the swirl number. However, the combustion literature has shown that axisymmetric structures (in contrast to helical structures) are often responsible for most of the heat release response. Therefore, this work performs a spatial stability analysis to study the swirl number sensitivity of the forced response of the axisymmetric mode. A spatio-temporal analysis is conducted in tandem to investigate the swirl number sensitivity of the impulse response of this mode. The results show that at low values of the swirl number, the axisymmetric mode stability is a weak function of the swirl number, but that new modes and stability bifurcations appear at high swirl numbers.
International Nuclear Information System (INIS)
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
Stability of limit cycles in autonomous nonlinear systems
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
2014-01-01
Roč. 49, č. 8 (2014), s. 1929-1943 ISSN 0025-6455 R&D Projects: GA AV ČR(CZ) IAA200710902; GA ČR(CZ) GA103/09/0094; GA ČR(CZ) GC13-34405J Institutional support: RVO:68378297 Keywords : limit cycle * nonlinear oscillator * stability Subject RIV: JM - Building Engineering Impact factor: 1.949, year: 2014 http://link.springer.com/article/10.1007/s11012-014-9899-8
Bifurcation and stability analysis of a nonlinear milling process
Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy
2018-01-01
Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.
Nonlinear Stability and Structure of Compressible Reacting Mixing Layers
Day, M. J.; Mansour, N. N.; Reynolds, W. C.
2000-01-01
The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers. Particular interest is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the 'outer' instability modes- one associated with each of the fast and slow streams-to dominate over the 'central', Kelvin-Helmholtz mode that unaccompanied in incompressible nonreacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompany these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central- mode vortex pairing, further supporting the view that pairing is primarily governed perspective sheds insight on how linear stability theory is able to provide such an accurate prediction of experimentally-observed, fully nonlinear flow phenomenon.
Burn Control in Fusion Reactors via Nonlinear Stabilization Techniques
International Nuclear Information System (INIS)
Schuster, Eugenio; Krstic, Miroslav; Tynan, George
2003-01-01
Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts on model-based control use control techniques for linear models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The subignition case, where the modulation of auxiliary power and fueling rate are considered as control forces, and the ignition case, where the controlled injection of impurities is considered as an additional actuator, are treated separately.The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by puffing. This imposed lag is treated using nonlinear backstepping.The nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers. In addition, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.The controller designed ensures setpoint regulation for the energy and plasma parameter β with robustness against uncertainties in the confinement times for different species. Hence, the controller can increase or decrease β, modify the power, the temperature or the density, and go from a subignition to an ignition point and vice versa
Absolute stability of nonlinear systems with time delays and applications to neural networks
Directory of Open Access Journals (Sweden)
Xinzhi Liu
2001-01-01
Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.
Kumawat, Tara Chand; Tiwari, Naveen
2018-03-01
Steady two-dimensional solutions and their stability analysis are presented for thin film of a thermoviscous liquid flowing inside a cylinder rotating about its horizontal axis. The inner surface of the cylinder is either uniformly hotter or colder than the enveloping air. The mass, momentum, and energy equations are simplified using thin-film approximation. The analytically obtained film thickness evolution equation consists of various dimensionless parameters such as gravitational number, Bond number, Biot number, thermoviscosity number, and Marangoni number. The viscosity of the liquid is considered as an exponential function of temperature. The viscosity increases (decreases) within the film thickness away from the inner surface of the cylinder when the surface is uniformly hotter (colder) than the atmosphere. For hotter (colder) surface, the film thickness on the rising side decreases (increases) when convective heat transfer at the free surface is increased. The surface tension gradient at the free surface generates Marangoni stress that has a destabilizing (stabilizing) effect on the thin film flow in the case of a hotter (colder) cylinder. The thermoviscosity number stabilizes (destabilizes) the flow on a heating (cooling) surface and this effect increases with an increase in the heat transfer at the free surface. For a hotter surface and in the presence of Marangoni stress, the convective heat transfer at the interface has the destabilizing effect for small values of the Biot number and assumes a stabilizing role for larger values. Non-linear simulations show consistency with the linear stability analysis.
A robust nonlinear stabilizer as a controller for improving transient stability in micro-grids.
Azimi, Seyed Mohammad; Afsharnia, Saeed
2017-01-01
This paper proposes a parametric-Lyapunov approach to the design of a stabilizer aimed at improving the transient stability of micro-grids (MGs). This strategy is applied to electronically-interfaced distributed resources (EI-DRs) operating with a unified control configuration applicable to all operational modes (i.e. grid-connected mode, islanded mode, and mode transitions). The proposed approach employs a simple structure compared with other nonlinear controllers, allowing ready implementation of the stabilizer. A new parametric-Lyapunov function is proposed rendering the proposed stabilizer more effective in damping system transition transients. The robustness of the proposed stabilizer is also verified based on both time-domain simulations and mathematical proofs, and an ultimate bound has been derived for the frequency transition transients. The proposed stabilizer operates by deploying solely local information and there are no needs for communication links. The deteriorating effects of the primary resource delays on the transient stability are also treated analytically. Finally, the effectiveness of the proposed stabilizer is evaluated through time-domain simulations and compared with the recently-developed stabilizers performed on a multi-resource MG. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
A Stability Analysis for a Hydrodynamic Three-Wave Journal Bearing
Ene, Nicoleta M.; Dimofte, Florin; Keith, Theo G., Jr.
2007-01-01
The influence of the wave amplitude and oil supply pressure on the dynamic behavior of a hydrodynamic three-wave journal bearing is presented. Both, a transient and a small perturbation technique, were used to predict the threshold to fractional frequency whirl (FFW). In addition, the behavior of the rotor after FFW appeared was determined from the transient analysis. The turbulent effects were also included in the computations. Bearings having a diameter of 30 mm, a length of 27.5 mm, and a clearance of 35 microns were analyzed. Numerical results were compared to experimental results obtained at the NASA GRC. Numerical and experimental results showed that the above-mentioned wave bearing with a wave amplitude ratio of 0.305 operates stably at rotational speeds up to 60,000 rpm, regardless of the oil supply pressure. For smaller wave amplitude ratios, a threshold of stability was found. It was observed that the threshold of stability for lower wave amplitude strongly depends on the oil supply pressure and on the wave amplitude. When the FFW occurs, the journal center maintains its trajectory inside the bearing clearance and therefore the rotor can be run safely without damaging the bearing surfaces.
How (non-)linear is the hydrodynamics of heavy ion collisions?
Energy Technology Data Exchange (ETDEWEB)
Floerchinger, Stefan; Wiedemann, Urs Achim [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Beraudo, Andrea [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Dep. de Fisica de Particulas, U. de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain); Del Zanna, Luca [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze (Italy); Inghirami, Gabriele [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); Rolando, Valentina [INFN - Sezione di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy); Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy)
2014-07-30
We provide evidence from full numerical solutions that the hydrodynamical evolution of initial density fluctuations in heavy ion collisions can be understood order-by-order in a perturbative series in deviations from a smooth and azimuthally symmetric background solution. To leading linear order, modes with different azimuthal wave numbers do not mix. When quadratic and higher order corrections are numerically sizable, they can be understood as overtones with corresponding wave numbers in a perturbative series. Several findings reported in the recent literature result naturally from the general perturbative series formulated here.
Directory of Open Access Journals (Sweden)
Diamandescu Aurel
2016-07-01
Full Text Available It is proved (necessary and sufficient conditions for Ψ– conditional exponential asymptotic stability of the trivial solution of nonlinear Lyapunov matrix differential equations
On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations
Directory of Open Access Journals (Sweden)
Diamandescu Aurel
2015-12-01
Full Text Available It is proved (necessary and sufficient conditions for Ψ − conditional asymptotic stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
On nonlinear stability in various random normed spaces
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Saadati Reza
2011-01-01
Full Text Available Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y + f ( 4 x - y = 3 0 6 9 f x + y 3 + f ( x + 2 y (1 + 1 3 6 f ( x - y - 1 3 9 4 f ( x + y + 4 2 5 f ( y - 1 5 3 0 f ( x (2 (3 in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.
Nonlinear flight dynamics and stability of hovering model insects
Liang, Bin; Sun, Mao
2013-01-01
Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714
Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt
2018-02-01
A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.
Evolutionary stability in continuous nonlinear public goods games.
Molina, Chai; Earn, David J D
2017-01-01
We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).
Directory of Open Access Journals (Sweden)
Wen-Tao Su
2014-03-01
Full Text Available This paper presents an experimental investigation of flow phenomena related to the characteristic frequencies of pressure fluctuation in Francis hydroturbine models. The experiments were carried out on two test rigs with two model runners having hydraulic similarities. Flow field around the guide vanes was measured with a particle image velocimetry (PIV on the first PIV test rig. Flow structures at the inlet region of runner and in draft tube at different operating conditions were visualized on another hydrodynamic test rig. Analyses of dominant frequency of unsteady hydraulic behaviors in the tested hydroturbines were performed. It was observed that the main frequency of flow over the guide vanes and the dominant frequency of channel vortex equal the blade passing frequency; the dominant frequency of flow separation at the suction side of blade inlet equals the vane passing frequency; the vortex rope in the draft tube displays a low-frequency nature. The flow instabilities and fluctuations directly influence the running of hydroturbine, thus these experimental results could provide important evidence for the stability study of a real hydroturbine.
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Faming Huang
2017-06-01
Full Text Available It is significant to study the variations in the stability coefficients of hydrodynamic pressure landslides with different permeability coefficients affected by reservoir water level fluctuations and rainstorms. The Sifangbei landslide in Three Gorges Reservoir area is used as case study. Its stability coefficients are simulated based on saturated-unsaturated seepage theory and finite element analysis. The operating conditions of stability coefficients calculation are reservoir water level variations between 175 m and 145 m, different rates of reservoir water level fluctuations, and a three-day continuous rainstorm. Results show that the stability coefficient of the hydrodynamic pressure landslide decreases with the drawdown of the reservoir water level, and a rapid drawdown rate leads to a small stability coefficient when the permeability coefficient ranges from 1.16 × 10−6 m/s to 4.64 × 10−5 m/s. Additionally, the landslide stability coefficient increases as the reservoir water level increases, and a rapid increase in the water level leads to a high stability coefficient when the permeability coefficient ranges from 1.16 × 10−6 m/s to 4.64 × 10−5 m/s. The landslide stability coefficient initially decreases and then increases as the reservoir water level declines when the permeability coefficient is greater than 4.64 × 10−5 m/s. Moreover, for structures with the same landslide, the landslide stability coefficient is most sensitive to the change in the rate of reservoir water level drawdown when the permeability coefficient increases from 1.16 × 10−6 m/s to 1.16 × 10−4 m/s. Additionally, the rate of decrease in the stability coefficient increases as the permeability coefficient increases. Finally, the three-day rainstorm leads to a significant reduction in landslide stability, and the rate of decrease in the stability coefficient initially increases and then decreases as the permeability coefficient increases.
Exponential stability of nonlinear time-varying differential equations and applications
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N. M. Linh
2001-05-01
Full Text Available In this paper, we give sufficient conditions for the exponential stability of a class of nonlinear time-varying differential equations. We use the Lyapunov method with functions that are not necessarily differentiable; hence we extend previous results. We also provide an application to exponential stability for nonlinear time-varying control systems.
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Xiaoguang Deng
2015-01-01
Full Text Available Based on the nonlinear stability analysis method, the 3D nonlinear finite element model of a composite girder cable-stayed bridge with three pylons is established to research the effect of factors including geometric nonlinearity, material nonlinearity, static wind load, and unbalanced construction load on the structural stability during construction. Besides, the structural nonlinear stability in different construction schemes and the determination of temporary pier position are also studied. The nonlinear stability safety factors are calculated to demonstrate the rationality and safety of construction schemes. The results show that the nonlinear stability safety factors of this bridge during construction meet the design requirement and the minimum value occurs in the maximum double cantilever stage. Besides, the nonlinear stability of the structure in the side of edge-pylon meets the design requirement in the two construction schemes. Furthermore, the temporary pier can improve the structure stability, effectively, and the actual position is reasonable. In addition, the local buckling of steel girder occurs earlier than overall instability under load in some cable tension stages. Finally, static wind load and the unbalanced construction load should be considered in the stability analysis for the adverse impact.
Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay
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S. J. Sadati
2010-01-01
Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.
Stabilization of solitons under competing nonlinearities by external potentials
Energy Technology Data Exchange (ETDEWEB)
Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-12-15
We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.
Yue, Chen; Seadawy, Aly; Lu, Dianchen
The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.
Directory of Open Access Journals (Sweden)
Chen Yue
2016-01-01
Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.
Hybrid fully nonlinear BEM-LBM numerical wave tank with applications in naval hydrodynamics
Mivehchi, Amin; Grilli, Stephan T.; Dahl, Jason M.; O'Reilly, Chris M.; Harris, Jeffrey C.; Kuznetsov, Konstantin; Janssen, Christian F.
2017-11-01
simulation of the complex dynamics response of ships in waves is typically modeled by nonlinear potential flow theory, usually solved with a higher order BEM. In some cases, the viscous/turbulent effects around a structure and in its wake need to be accurately modeled to capture the salient physics of the problem. Here, we present a fully 3D model based on a hybrid perturbation method. In this method, the velocity and pressure are decomposed as the sum of an inviscid flow and viscous perturbation. The inviscid part is solved over the whole domain using a BEM based on cubic spline element. These inviscid results are then used to force a near-field perturbation solution on a smaller domain size, which is solved with a NS model based on LBM-LES, and implemented on GPUs. The BEM solution for large grids is greatly accelerated by using a parallelized FMM, which is efficiently implemented on large and small clusters, yielding an almost linear scaling with the number of unknowns. A new representation of corners and edges is implemented, which improves the global accuracy of the BEM solver, particularly for moving boundaries. We present model results and the recent improvements of the BEM, alongside results of the hybrid model, for applications to problems. Office of Naval Research Grants N000141310687 and N000141612970.
2014-01-01
This paper provides improved time delay-dependent stability criteria for multi-input and multi-output (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to demonstrate the effectiveness of the proposed stability condition. PMID:24744679
Stabilization and regulation of nonlinear systems a robust and adaptive approach
Chen, Zhiyong
2015-01-01
The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
Stability and square integrability of solutions of nonlinear fourth order differential equations
Directory of Open Access Journals (Sweden)
Moussadek Remili
2016-05-01
Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
International Nuclear Information System (INIS)
Chattopadhyay, S.; Audy, P.; Courant, E.D.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Antonie Arij; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched
Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping
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Eleni Bisognin
2007-01-01
Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.
Sadri, Sobhan; Wu, Christine
2013-06-01
For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.
Zhai, Junyong; Du, Haibo
2013-03-01
This paper investigates the problem of semi-global stabilization by output feedback for a class of nonlinear systems using homogeneous domination approach. For each subsystem, we first design an output feedback stabilizer for the nominal system without the perturbing nonlinearities. Then, based on the ideas of the homogeneous systems theory and the adding a power integrator technique, a series of homogeneous output feedback stabilizers are constructed recursively for each subsystem and the closed-loop system is rendered semi-globally asymptotically stable. The efficiency of the output feedback stabilizers is demonstrated by a simulation example. Crown Copyright © 2012. Published by Elsevier Ltd. All rights reserved.
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...... dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function....
Hydrodynamic processes and the stability of intertidal mussel beds in the Dutch Wadden Sea
Donker, J.J.A.
2015-01-01
The mussel population in the Dutch Wadden Sea, especially in the Western parts, is currently under pressure. Hydrodynamic process influence intertidal mussel beds in two ways: on the one hand currents are responsible for the transfer of food and sediments towards the beds, on the other hand, large
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
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Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
Directory of Open Access Journals (Sweden)
Breńkacz Łukasz
2017-12-01
Full Text Available Hydrodynamic bearings are commonly used in ship propulsion systems. Typically, they are calculated using numerical or experimental methods. This paper presents an experimental study through which it has been possible to estimate 24 dynamic coefficients of two hydrodynamic slide bearings operating under nonlinear conditions. During the investigation, bearing mass coefficients are identified by means of a newly developed algorithm. An impact hammer was used to excite vibration of the shaft. The approximation by means of the least squares method was applied to determine bearing dynamic coefficients. Based on the performed research, the four (i.e. two main and two crosscoupled coefficients of stiffness, damping and mass for each bearing were obtained. The mass coefficients add up to the complex shaft weight. These values are not required for modeling dynamics of the machine because the rotor mass is usually known, however, they may serve as a good indicator to validate the correctness of the stiffness and damping coefficients determined. Additionally, the experimental research procedure was described. The signals of displacements in the bearings and the excitation forces used for determination of the bearing dynamic coefficients were shown. The study discussed in this article is about a rotor supported by two hydrodynamic bearings operating in a nonlinear manner. On the basis of computations, the results of bearing dynamic coefficients were presented for a selected speed.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications
Kuehl, Joseph J.
2017-02-01
A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.
Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2
Mohler, R. R.
1992-01-01
This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.
Nonlinear behaviour and stability of thin-walled shells
Obodan, Natalia I; Gromov, Vasilii A
2013-01-01
This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings. The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem. A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.
A geometric criterion for the stability of forced oscillations in non-linear mechanics (1961)
International Nuclear Information System (INIS)
Blaquiere, A.
1961-01-01
The author completes the two-parameter diagram theory which he has previously explained, by giving a geometric criterion of stability for a non-linear system under forced conditions. After two simple geometric transformations of the diagram he obtains the separators which are the boundary conditions for the zones of stability. (author) [fr
Results on stabilization of nonlinear systems under finite data-rate constraints
Persis, Claudio De
2004-01-01
We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when
Gil', M. I.
2005-08-01
We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
On the nonlinear stability of mKdV breathers
DEFF Research Database (Denmark)
Alejo Plana, Miguel Angel; Muñoz, Claudio
2012-01-01
Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under...
Stability of one-step methods in transient nonlinear heat conduction
International Nuclear Information System (INIS)
Hughes, J.R.
1977-01-01
The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. In this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability critierion for the linear, constant coefficient case. However, for nonlinear problems there are differences and theses ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are equivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are: The stability behaviour of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified. All notions of stability employed are motivated and defined, and their interpretations in practical computing are indicated. (Auth.)
Stability of one-step methods in transient nonlinear heat conduction
International Nuclear Information System (INIS)
Hughes, J.R.
1977-01-01
The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. The class of problems considered is governed by a temporally continuous, spatially discrete system involving the capacity matrix C, conductivity matrix K, heat supply vector, temperature vector and time differenciation. In the linear case, in which K and C are constant, the stability behavior of one-step methods is well known. But in this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability criterion for the linear, constant coefficient case. However, for nonlinear problems there are differences and these ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are quivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are summarized as follows. The stability behavior of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified
Preservation of stability and synchronization in nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Anaya, G. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: guillermo.fernandez@uia.mx; Flores-Godoy, J.J. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: job.flores@uia.mx; Femat, R. [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055, Col. Lomas 4a. seccion, San Luis Potosi, San Luis Potosi 78216 (Mexico)], E-mail: rfemat@ipicyt.edu.mx; Alvarez-Ramirez, J.J. [Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico)], E-mail: jjar@xanum.uam.mx
2007-11-12
Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.
Preservation of stability and synchronization in nonlinear systems
International Nuclear Information System (INIS)
Fernandez-Anaya, G.; Flores-Godoy, J.J.; Femat, R.; Alvarez-Ramirez, J.J.
2007-01-01
Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results
Lagrangian approach to weakly nonlinear stability of elliptical flow
International Nuclear Information System (INIS)
Fukumoto, Y; Mie, Y; Hirota, M
2010-01-01
Rotating flows with elliptically strained streamlines suffer from parametric resonance instability between a pair of Kelvin waves whose azimuthal wavenumbers are separated by two. We address the weakly nonlinear amplitude evolution of three-dimensional (3D) Kelvin waves, in resonance, on a flow confined in a cylinder of elliptic cross-section. In a traditional Eulerian approach, derivation of the mean flow induced by nonlinear interaction of Kelvin waves stands as an obstacle. We show how a topological idea, or the Lagrangian approach, facilitates calculation of the wave-induced mean flow. A steady incompressible Euler flow is characterized as a state of the maximum of the total kinetic energy with respect to perturbations constrained to an isovortical sheet, and the isovortical perturbation is handled only in terms of the Lagrangian variables. The criticality in energy of a steady flow allows us to calculate the wave-induced mean flow only from the linear Lagrangian displacement. With the mean flow at hand, the Lagrangian approach provides us with a shortcut to enter into a weakly nonlinear amplitude evolution regime of 3D disturbances. Unlike the Eulerian approach, the amplitude equations are available directly in the Hamiltonian normal form.
Dagan, Yuval; Ghoniem, Ahmed
2017-11-01
Recent experimental observations show that the dynamic response of a reactive flow is strongly impacted by the fuel chemistry. In order to gain insight into some of the underlying mechanisms we formulate a new linear stability model that incorporates the impact of finite rate chemistry on the hydrodynamic stability of shear flows. Contrary to previous studies which typically assume that the velocity field is independent of the kinetic rates, the velocity field in our study is coupled with the temperature field. Using this formulation, we reproduce previous results, e.g., most unstable global modes, obtained for non-reacting shear flow. Moreover, we show that these modes are significantly altered in frequency and gain by the presence of a reaction region within the shear layer. This qualitatively agrees with results of our recent experimental and numerical studies, which show that the flame surface location relative to the shear layer influences the stability characteristics in combustion tunnels. This study suggests a physical explanation for the observed impact of finite rate chemistry on shear flow stability.
SPORTS - a simple non-linear thermalhydraulic stability code
International Nuclear Information System (INIS)
Chatoorgoon, V.
1986-01-01
A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)
Stabilization of nonlinear system using uniform eigenvalue assignment in linear model
Siahaan, Sahat P.; Pangaribuan, Timbang
2017-09-01
Some plant in control system has nonlinear dynamic, so it is not easy to do in analysis to see its behavior using eigenstructure assignment. From many observations which have been made, some literature give methods to design nonlinear control system. The modern control theory uses state-space method to explain the behaviour on stability of a plant. To improve the stability of the closed-loop system, designer commonly use the state feedback control law. For the case inverted pendulum plant with the nonlinear dynamics, its need to perform the nonlinear control law with the concepts of modern control theory to satisfy the closed-loop system characteristic, and all the behaviour of the closed-loop system only determined from the given linear pole specifications.
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-01-01
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms. PMID:25978877
Nonlinear drift tearing mode. Strong mode of excitation and stabilization mechanisms
International Nuclear Information System (INIS)
Galeev, A.A.; Zelenyj, L.M.; Kuznetsova, M.M.
1985-01-01
A nonlinear theory of magnetic disturbance development in collisionless configurations with magnetic field shear is considered. The instability evolution is investigated with account for the dynamics of ions and potential electric fields which determine the mode stabilization. It has been found that the drift tearing mode possesses metastable properties: in a nonlinear mode even the growth of linearly stable disturbances of the finite amplitude is possible
Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2
International Nuclear Information System (INIS)
Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.
1980-07-01
The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt
Algorithmic Approximation of Optimal Value Differential Stability Bounds in Nonlinear Programming,
1981-08-01
NCLASSIFIED RANO/PA6659 N IN *~4 112.0.0 ~11111,.. I32 111 IIIII 111111.25 MICROCOPY RESOLUTION TESI CHART NATIOt AL BJRLAU Of SIANDARD 1964 A * LEVEL 00 o pm...Sensitivity Analysis in Parametric Nonlinear Programming, Doctoral Dissertation, School of Engineering and Applied Science, The George Washington University...Differential Stability of the Optimal Value Function in Constrained Nonlinear Programing, Doctoral Disser- tation, School of Engineering and Applied
Stability analysis for stochastic BAM nonlinear neural network with delays
Lv, Z. W.; Shu, H. S.; Wei, G. L.
2008-02-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.
Helical vortices: linear stability analysis and nonlinear dynamics
Selçuk, C.; Delbende, I.; Rossi, M.
2018-02-01
We numerically investigate, within the context of helical symmetry, the dynamics of a regular array of two or three helical vortices with or without a straight central hub vortex. The Navier–Stokes equations are linearised to study the instabilities of such basic states. For vortices with low pitches, an unstable mode is extracted which corresponds to a displacement mode and growth rates are found to compare well with results valid for an infinite row of point vortices or an infinite alley of vortex rings. For larger pitches, the system is stable with respect to helically symmetric perturbations. In the nonlinear regime, we follow the time-evolution of the above basic states when initially perturbed by the dominant instability mode. For two vortices, sequences of overtaking events, leapfrogging and eventually merging are observed. The transition between such behaviours occurs at a critical ratio involving the core size and the vortex-separation distance. Cases with three helical vortices are also presented.
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
Local asymptotic stability for nonlinear quadratic functional integral equations
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2008-03-01
Full Text Available In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Czech Academy of Sciences Publication Activity Database
Mordukhovich, B. S.; Outrata, Jiří
2013-01-01
Roč. 49, č. 3 (2013), s. 446-464 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : variational analysis * second-order theory * generalized differentiation * tilt stability Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-tilt stability in nonlinear programming under mangasarian-fromovitz constraint qualification.pdf
Nonlinear stability research on the hydraulic system of double-side rolling shear
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.
Schuller, F. T.
1973-01-01
This publication is the result of over 260 fractional-frequency-whirl stability tests on a variety of fixed-geometry journal bearings. It is intended principally as a guide in the selection and design of antiwhirl bearings that must operate at high speeds and low loads in low-viscosity fluids such as water or liquid metals. However, the various fixed-geometry configurations can be employed as well in applications where other lubricants, such as oil, are used and fractional-frequency whirl is a problem. The important parameters that effect stability are discussed for each bearing type, and design curves to facilitate the design of optimum-geometry bearings are included. A comparison of the stability of the different bearing configurations tested is also given.
Energy Technology Data Exchange (ETDEWEB)
Tentner, A. [Argonne National Lab. (ANL), Argonne, IL (United States); Bojanowski, C. [Argonne National Lab. (ANL), Argonne, IL (United States); Feldman, E. [Argonne National Lab. (ANL), Argonne, IL (United States); Wilson, E. [Argonne National Lab. (ANL), Argonne, IL (United States); Solbrekken, G [Univ. of Missouri, Columbia, MO (United States); Jesse, C. [Univ. of Missouri, Columbia, MO (United States); Kennedy, J. [Univ. of Missouri, Columbia, MO (United States); Rivers, J. [Univ. of Missouri, Columbia, MO (United States); Schnieders, G. [Univ. of Missouri, Columbia, MO (United States)
2017-05-01
An experimental and computational effort was undertaken in order to evaluate the capability of the fluid-structure interaction (FSI) simulation tools to describe the deflection of a Missouri University Research Reactor (MURR) fuel element plate redesigned for conversion to lowenriched uranium (LEU) fuel due to hydrodynamic forces. Experiments involving both flat plates and curved plates were conducted in a water flow test loop located at the University of Missouri (MU), at conditions and geometries that can be related to the MURR LEU fuel element. A wider channel gap on one side of the test plate, and a narrower on the other represent the differences that could be encountered in a MURR element due to allowed fabrication variability. The difference in the channel gaps leads to a pressure differential across the plate, leading to plate deflection. The induced plate deflection the pressure difference induces in the plate was measured at specified locations using a laser measurement technique. High fidelity 3-D simulations of the experiments were performed at MU using the computational fluid dynamics code STAR-CCM+ coupled with the structural mechanics code ABAQUS. Independent simulations of the experiments were performed at Argonne National Laboratory (ANL) using the STAR-CCM+ code and its built-in structural mechanics solver. The simulation results obtained at MU and ANL were compared with the corresponding measured plate deflections.
Frequency stabilization in nonlinear MEMS and NEMS oscillators
Lopez, Omar Daniel; Antonio, Dario
2014-09-16
An illustrative system includes an amplifier operably connected to a phase shifter. The amplifier is configured to amplify a voltage from an oscillator. The phase shifter is operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage and is configured to set an amplitude of the phase shifted voltage. The oscillator is operably connected to the driving amplitude control. The phase shifted voltage drives the oscillator. The oscillator is at an internal resonance condition, based at least on the amplitude of the phase shifted voltage, that stabilizes frequency oscillations in the oscillator.
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control
Ramirez, Hector; Zwart, Hans; Le Gorrec, Yann
2017-01-01
The conditions for existence of solutions and stability, asymptotic and exponential, of a large class of boundary controlled systems on a 1D spatial domain subject to nonlinear dynamic boundary actuation are given. The consideration of such class of control systems is motivated by the use of
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Stabilization of the higher order nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
18
Abstract. We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. ... cattering, respectively. (1.2) also arised in the optical communications (see [1, 8, 16]). They can be applied to the long distance communications and ultrafast signalrouting systems. The HNLS models.
Linear and nonlinear stability of periodic orbits in annular billiards.
Dettmann, Carl P; Fain, Vitaly
2017-04-01
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Suming; Nie, Zongxiu
2014-11-01
Paul trap working in the second stability region has long been recognized as a possible approach for achieving high-resolution mass spectrometry (MS), which however is still far away from the experimental implementations because of the narrow working area and inefficient ion trapping. Full understanding of the ion motional behavior is helpful for solving the problem. In this article, the ion motion in a superimposed octopole field, which was characterized by the nonlinear Mathieu equation, was solved analytically using Poincare-Lighthill-Kuo (PLK) method. This method equivalently described the nonlinear disturbance by an effective quadrupole field with perturbed Mathieu parameters, a(u) and q(u), which would bring huge convenience in the studies of nonlinear ion dynamics and was, therefore, used for rapid evaluation of the nonlinear effects of ion motion. Fourth-order Runge-Kutta method (4th R-K) indicated the error of PLK for characterizing the frequency shift of ion motion was within 15%.
Hartig, Florian; Münkemüller, Tamara; Johst, Karin; Dieckmann, Ulf
2014-01-01
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and
Directory of Open Access Journals (Sweden)
Ali Ben Moussa
2012-10-01
Full Text Available In this work, the problem of hydrodynamic, heat and mass transfer and stability in a salt gradient solar pond has been numerically studied by means of computational fluid dynamics in transient regime. The body of the simulated pond is an enclosure of height H and length L wherein an artificial salinity gradient is created in order to suppress convective motions induced by solar radiation absorption and to stabilize the solar pond during the period of operation. Here we show the distribution of velocity, temperature and salt concentration fields during energy collection and storage in a solar pond filled with water and constituted by three different salinity zones. The bottom of the pond is blackened and the free-surface is subjected to heat losses by convection, evaporation and radiation while the vertical walls are adiabatic and impermeable. The governing equations of continuity, momentum, thermal energy and mass transfer are discretized by finite–volume method in transient regime. Velocity vector fields show the presence of thin convective cells in the upper convective zone (UCZ and large convective cells in the lower convective zone (LCZ. This study shows the importance of buoyancy ratio in the decrease of temperature in the UCZ and in the preservation of high temperature in the LCZ. It shows also the importance of the thickness of Non-Convective Zone (NCZ in the reduction of the upwards heat losses.
Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying
2018-04-01
The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.
Study of the hydrodynamic stability of natural-circulation steam generators
International Nuclear Information System (INIS)
Olive, J.
1981-01-01
This report presents a mathematical model of a study of the stability of natural-circulation steam generators. The method used consists in linearizing the equations for the single-dimensional flow and integrating them by using Laplace's transformation. The properties of the two-phase fluids are described by a homegeneous model with slip. The results of the calculation are the transfer functions of the circulation loop and its own oscillation modes (period and damping). Comparison of the results obtained by this method with those from other existing methods in the case of a straight tube with forced flow have proved satisfactory. Lastly, the results of a parametric study on the stability of a natural-circulation steam generator for a PWR unit are presented. The results show that the model is capable of reproducing at least qualitatively the trends observed experimentally or obtained by other more complex theoretical models [fr
Expansion methods for finding nonlinear stability domains of nuclear reactor models
International Nuclear Information System (INIS)
Yang, C.Y.; Cho, N.Z.
1992-01-01
Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are described in this paper: Method A based on expansion of a Lyapunov function and Method B based on expansion of any positive definite function. The methods are established on Lyapunov's stability definitions. Method A provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most reactor systems are stiff. Method B requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for reactor systems that are stiff. These methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. (author)
Nonlinear analysis of dynamic stability for the thin cylindrical shells of supercavitating vehicles
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Hai An
2016-12-01
Full Text Available The dynamic stability of supercavitating vehicles under periodic axial loading is investigated in this article. The supercavitating vehicle is simulated as a long and thin cylindrical shell subjected to periodic axial loading and simply supported boundary conditions. The nonlinear transverse vibration differential equation is obtained in terms of nonlinear geometric equations, physical equations, and balance equations of cylindrical shells. Mathieu equation with periodic coefficients and nonlinear term is derived by employing Galerkin variational method and Bolotin method. The analytical expressions of the steady-state amplitudes of vibrations in the first- and second-order instable regions are obtained by solving nonlinear Mathieu equation derived in this article. Numerical results are presented to analyze the influence of the sailing speed, ratio of loads, the frequency of axial loads, and the mode of vibration on parametric resonance curves and to show the nonlinear parametric resonance curves incline toward the side where it is greater than the excitation frequency, which significantly extends the range of the exciting region. The presented results indicate the enlargement of the exciting region will cause shrinkage of the safe frequency range of external loads and decrease in dynamic stability of supercavitating vehicle.
Nonlinear MHD simulations of the gravitational ballooning mode close to marginal stability
International Nuclear Information System (INIS)
Myers, S A; Dudson, B D; Wilson, H R
2013-01-01
The ballooning mode is thought to play a key role in the mechanism which drives the problematic edge localized modes in tokamak plasmas, and possibly in other plasma eruptions, such as in the magnetosphere. We investigate the essential nonlinear physics of this mode by simulating an instability driven by gravity in a slab of magnetized plasma; magnetic field curvature plays a similar role in toroidal confinement systems. Full ideal magnetohydrodynamics (MHD) simulations are performed, which exhibit three distinct phases of the mode's evolution: (I) a linear phase that agrees well with the predictions of linear ideal MHD; (II) a non-linear regime where the instantaneous growth rate evolves, and is somewhat lower than the linear value and (III) an explosive plasma eruption. These regimes are characterized and compared with the predictions of analytic nonlinear theory, considering cases that are close to and far from marginal stability. Evidence of a subcritical instability is demonstrated in phase II where, provided the mode's amplitude is large enough, it can develop into an eruption even for values of gravity that give linear stability. The drop in growth rate during phase II depends on the strength of the linear drive, demonstrating that the initial phases of the nonlinear evolution are also dependent on the strength of the linear drive. To extend the calculations deeper into the nonlinear regime a four-field reduced MHD model is developed, which reproduces the same features as the full ideal MHD system. (paper)
Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing
Directory of Open Access Journals (Sweden)
Chang Chuan Xie
2008-01-01
Full Text Available A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN, and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.
Comparison of magnetic island stabilization strategies from magneto-hydrodynamic simulations
Février, O.; Maget, P.; Lütjens, H.; Beyer, P.
2017-04-01
The degradation of plasma confinement in tokamaks caused by magnetic islands motivates to better understand their possible suppression using electron cyclotron current drive (ECCD) and to investigate the various strategies relevant for this purpose. In this work, we evaluate the efficiency of several control methods through nonlinear simulations of this process with the toroidal magneto-hydro-dynamic (MHD) code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130-43), which has been extended to incorporate in Ohm’s law a source term modeling the driven current resulting from the interaction of the EC waves with the plasma. A basic control system has been implemented in the code, allowing testing of advanced strategies that require feedback on island position or phase. We focus in particular on the robustness of the control strategies towards uncertainties that apply to the control and ECCD systems, such as the risk of misalignment of the current deposition or the possible inability to generate narrow current deposition.
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Hui Ye
2017-01-01
Full Text Available This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs. The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.
Freed, Alan; Leonov, Arkady I.
2002-01-01
This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.
Controlling the stability of nonlinear optical modes via electromagnetically induced transparency
Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun
2018-02-01
We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.
International Nuclear Information System (INIS)
Cheng, Po-Jen; Chen, Cha'o-Kuang; Lai, Hsin-Yi
2001-01-01
This article investigates the weakly nonlinear stability theory of a thin pseudoplastic liquid film flowing down on a vertical wall. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equation with free film interface. The normal mode approach is used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg - Landau equation. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a pseudoplastic film flow system. The results also reveal that the pseudoplastic liquid film flows are less stable than Newtonian's as traveling down along the vertical wall. The degree of instability in the film flow is further intensified by decreasing the flow index n. [copyright] 2001 American Institute of Physics
Li, B O; Sun, Hui; Zhou, Shenggao
The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.
Stability and stabilization of nonlinear systems and Takagi-Sugeno's fuzzy models
Directory of Open Access Journals (Sweden)
Blanco Yann
2001-01-01
Full Text Available This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC. An application to the inverted pendulum is proposed here.
Directory of Open Access Journals (Sweden)
Xinhua Zheng
2015-01-01
Full Text Available Stability of pneumatic cabin pressure regulating system with complex nonlinear characteristics is considered. The mathematical model of each component is obtained and given in detail. The governing equations of the considered system consist of 8 differential equations. In the circumstance, commonly used methods of nonlinear system analysis are not applicable. Therefore a new method is proposed to construct phase plane trajectories numerically. The calculation steps are given in detail. And convergence region of numerical calculation and limits on step size is defined. The method is applied constructing phase plane trajectories for considered cabin pressure regulating system. Phase plane analysis shows that there exists a limit cycle, which is responsible for pressure pulsating in aircraft cabin. After parameters adjustment, excellent stability characteristics are acquired. And the validity of this method is confirmed by the simulation.
Nonlinear ω*-stabilization of the m = 1 mode in tokamaks
International Nuclear Information System (INIS)
Rogers, B.; Zakharov, L.
1995-08-01
Earlier studies of sawtooth oscillations in Tokamak Fusion Test Reactor supershots (Levinton et al, Phys. Rev. Lett. 72, 2895 (1994); Zakharov, et al, Plasma Phys. and Contr. Nucl. Fus. Res., Proc. 15th Int. Conf., Seville 1994, Vienna) have found an apparent contradiction between conventional linear theory and experiment: even in sawtooth-free discharges, the theory typically predicts instability due to a nearly ideal m = 1 mode. Here, the nonlinear evolution of such mode is analyzed using numerical simulations of a two-fluid magnetohydrodynamic (MHD) model. We find the mode saturates nonlinearly at a small amplitude provided the ion and electron drift-frequencies ω* i,e are somewhat above the linear stability threshold of the collisionless m = 1 reconnecting mode. The comparison of the simulation results to m = 1 mode activity in TFTR suggests additional, stabilizing effects outside the present model are also important
Scheme for improving laser stability via feedback control of intracavity nonlinear loss.
Jin, Pixian; Lu, Huadong; Su, Jing; Peng, Kunchi
2016-05-01
We present a novel and efficient scheme to enhance the stability of laser output via feedback control to a nonlinear loss deliberately introduced to the laser resonator. By means of the feedback control to the intracavity nonlinear loss of an all-solid-state continuous-wave single-frequency laser with high output power at 1064 nm, its intensity and frequency stabilities are significantly improved. A lithium triborate crystal is deliberately placed inside the laser resonator to be an element of the nonlinear loss, and the temperature of the crystal is feedback controlled by an electronic loop. The control signal is generated by distinguishing the deviation of the output power and used for manipulating the intracavity nonlinear loss to compensate the deviation of the laser power actively. With the feedback-control loop, the intensity and frequency fluctuations of the output laser at 1064 nm are reduced from ±0.59% and 21.82 MHz without the feedback to ±0.26% and 9.84 MHz, respectively.
Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan
2014-07-01
The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.
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Huang Tingwen
2009-01-01
Full Text Available This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.
Existence and stability of the externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
The externally driven damped nonlinear Schroedinger (NLS) equation on the infinite line is studied. Existence and stability chart for its soliton solution is constructed on the plane of two control parameters, the forcing amplitude h and dissipation coefficient γ. For generic values of h and γ there are two coexisting solitons one of which (ψ + ) is always unstable. The bifurcation diagram of the second solution (ψ - ) depends on the dissipation coefficient: if γ cr , the ψ - is stable for small h and loses its stability via a Hopf bifurcation as h is increased; if γ>γ cr , the ψ - is stable for all h. There are no 'stability windows' in the unstable region. We show that the previously reported 'stability windows' occur only when the equation is considered on a finite (and small) spatial interval
Directory of Open Access Journals (Sweden)
Sherif Amirov
2017-08-01
Full Text Available The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points.
Existence and Stability of the Solution of a Nonlinear Boundary Value Problem
Directory of Open Access Journals (Sweden)
Agneta M. Balint
2012-01-01
Full Text Available The purpose is to find conditions assuring the existence of solutions for a nonlinear, boundary value problem in case of the axis-symmetric Young-Laplace differential equation. The equation describes the capillary surface between two static fluids. Necessary or sufficient conditions are found for the existence of a solution. The static stability of the obtained solution is also analyzed and stability or instability results are revealed. For the NdYAG microfiber growth, by the pulling-down method, numerical illustrations are given.
Electro-optic side-chain polyimide system with large optical nonlinearity and high thermal stability
Sotoyama, Wataru; Tatsuura, Satoshi; Yoshimura, Tetsuzo
1994-04-01
We report electro-optic (EO) efficiency and thermal stability of a poled polyimide system with nonlinear optical dyes as side chains. The side-chain polyimide system is synthesized from a dianhydride containing azobenzene dye and a diamine. The dye in the polymer is chemically stable for temperatures below 250 °C. The polymer can be poled simultaneously with or after imidization of the polyamic acid. Our sample poled after imidization shows a large EO coefficient (r33=10.8 pm/V at λ=1.3 μm) and long-term thermal stability at 120 °C.
Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei
2017-01-01
The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.
On the internal stability of non-linear dynamic inversion: application to flight control
Czech Academy of Sciences Publication Activity Database
Alam, M.; Čelikovský, Sergej
2017-01-01
Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf
Dynamic stability of a vertically excited non-linear continuous system
Czech Academy of Sciences Publication Activity Database
Náprstek, Jiří; Fischer, Cyril
2015-01-01
Roč. 155, July (2015), s. 106-114 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear systems * auto-parametric systems * semi-trivial solution * dynamic stability * system recovery * post- critical response Subject RIV: JM - Building Engineering Impact factor: 2.425, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045794915000024
A nonlinear two-species oscillatory system: bifurcation and stability analysis
Directory of Open Access Journals (Sweden)
C. G. Chakrabarti
2003-06-01
Full Text Available The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.
International Nuclear Information System (INIS)
Zhang Tie-Yan; Zhao Yan; Xie Xiang-Peng
2012-01-01
This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach. (general)
Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays
Nguimdo, Romain Modeste
2018-03-01
Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.
Nonlinear stability and control study of highly maneuverable high performance aircraft
Mohler, R. R.
1993-01-01
This project is intended to research and develop new nonlinear methodologies for the control and stability analysis of high-performance, high angle-of-attack aircraft such as HARV (F18). Past research (reported in our Phase 1, 2, and 3 progress reports) is summarized and more details of final Phase 3 research is provided. While research emphasis is on nonlinear control, other tasks such as associated model development, system identification, stability analysis, and simulation are performed in some detail as well. An overview of various models that were investigated for different purposes such as an approximate model reference for control adaptation, as well as another model for accurate rigid-body longitudinal motion is provided. Only a very cursory analysis was made relative to type 8 (flexible body dynamics). Standard nonlinear longitudinal airframe dynamics (type 7) with the available modified F18 stability derivatives, thrust vectoring, actuator dynamics, and control constraints are utilized for simulated flight evaluation of derived controller performance in all cases studied.
Linear and nonlinear stability analysis in BWRs applying a reduced order model
Energy Technology Data Exchange (ETDEWEB)
Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)
2016-09-15
Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)
Krishnan, Hariharan
1993-01-01
This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude
Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses
International Nuclear Information System (INIS)
March-Leuba, J.; Cacuci, D.G.; Perez, R.B.
1985-01-01
A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations
Directory of Open Access Journals (Sweden)
Ricardo A. da Mota Silveira
Full Text Available AbstractThis paper presents a nonlinear stability analysis of piles under bilateral contact constraints imposed by a geological medium (soil or rock. To solve this contact problem, the paper proposes a general numerical methodology, based on the finite element method (FEM. In this context, a geometrically nonlinear beam-column element is used to model the pile while the geological medium can be idealized as discrete (spring or continuum (Winkler and Pasternak foundation elements. Foundation elements are supposed to react under tension and compression, so during the deformation process the structural elements are subjected to bilateral contact constraints. The errors along the equilibrium paths are minimized and the convoluted nonlinear equilibrium paths are made traceable through the use of an updated Lagrangian formulation and a Newton-Raphson scheme working with the generalized displacement technique. The study offers stability analyses of three problems involving piles under bilateral contact constraints. The analyses show that in the evaluation of critical loads a great influence is wielded by the instability modes. Also, the structural system stiffness can be highly influenced by the representative model of the soil.
Stability Analysis and Design of a Nonlinear Controller for Hot Rolling Coiler
Directory of Open Access Journals (Sweden)
Rui Li
2015-01-01
Full Text Available For the new style hot rolling coiler which adopt AC asynchronous motor as the driving force and with using the algorithm based on differential geometry design nonlinear controller, precise coiling tension control in the rolling process of strip steel is achieved. In this paper, under the rotating orthogonal coordinate system, the fifth-order nonlinear motor model is selected as the controlled plant. By multi-input multioutput (MIMO exact feedback linearization (EFL algorithm, the nonlinear model is transformed to a linear one. In terms of small-gain theorem, it is the first to prove that the nonlinear coiler engine that contains the controller has characteristics of input-to-state stability. Experimental results show that the algorithm can be used for high order tracking control system with time-varying parameters. Even without the traditional flux orientation calculation, the output signals are decoupled. With this controller, the tension deviation is restricted to less than 3% and average rotational speed bias was decreased from 0.5% to 0.1% that ensure high-quality plate cut and surface of strip products.
International Nuclear Information System (INIS)
Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
Soliton stability criterion for generalized nonlinear Schrödinger equations.
Quintero, Niurka R; Mertens, Franz G; Bishop, A R
2015-01-01
A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed.
Stabilization of business cycles of finance agents using nonlinear optimal control
Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.
2017-11-01
Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.
Study of static and dynamic stability of flexible rods in a geometrically nonlinear statement
Annin, B. D.; Vlasov, A. Yu.; Zakharov, Yu. V.; Okhotkin, K. G.
2017-07-01
We study static and dynamic stability problems for a thin flexible rod subjected to axial compression with the geometric nonlinearity explicitly taken into account. In the case of static action of a force, the critical load and the bending shapes of the rod were determined by Euler. Lavrent'ev and Ishlinsky discovered that, in the case of rod dynamic loading significantly greater than the Euler static critical load, there arise buckling modes with a large number of waves in the longitudinal direction. Lavrent'ev and Ishlinsky referred to the first loading threshold discovered by Euler as the static threshold, and the subsequent ones were called dynamic thresholds; they can be attained under impact loading if the pulse growth time is less than the system relaxation time. Later, the buckling mechanism in this case and the arising parametric resonance were studied in detail by Academician Morozov and his colleagues. In this paper, we complete and develop the approach to studying dynamic rod systems suggested by Morozov; in particular, we construct exact and approximate analytic solutions by using a system of special functions generalizing the Jacobi elliptic functions. We obtain approximate analytic solutions of the nonlinear dynamic problem of flexible rod deformation under longitudinal loading with regard to the boundary conditions and show that the analytic solution of static rod system stability problems in a geometrically nonlinear statement permits exactly determining all possible shapes of the bent rod and the complete system of buckling thresholds. The study of approximate analytic solutions of dynamic problems of nonlinear vibrations of rod systems loaded by lumped forces after buckling in the deformed state allows one to determine the vibration frequencies and then the parametric resonance thresholds.
Large Signal Stabilization of Hybrid AC/DC Micro-Grids Using Nonlinear Robust Controller
Directory of Open Access Journals (Sweden)
Reza Pejmanfar
2017-12-01
Full Text Available This paper presents a robust nonlinear integrated controller to improve stability of hybrid AC/DC micro-grids under islanding mode. The proposed controller includes two independent controllers where each one is responsible to control one part of the system. First controller will improve the stability of input DC/DC converter. Using this controller, the voltage of DC bus is fully stabilized such that when a large disturbance occurs, its voltage will become constant without any significant dynamic. The necessity of DC bus regulation which has not been considered in previous studies, is imminent as it not only improves voltage stability of the micro-grid but also protects consumers which are directly connected to the DC bus, against voltage variations. Frequency stability of the micro-grid is provided by the second proposed controller which is applied to output DC/AC converter of the micro-grid. Adaptive method is used to make the controllers proposed in this paper, robust. Duty cycle of converters switches are adjusted such that voltage and frequency of the micro-grid are set on the desired value in minimum possible time under transient disturbances and uncertainty of the loads as well as micro-sources characteristics.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials
International Nuclear Information System (INIS)
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Guenter, Peter
2008-01-01
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-(3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene) malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites
Existence, Stability and Dynamics of Nonlinear Modes in a 2D PartiallyPT Symmetric Potential
Directory of Open Access Journals (Sweden)
Jennie D’Ambroise
2017-02-01
Full Text Available It is known that multidimensional complex potentials obeying parity-time(PTsymmetry may possess all real spectra and continuous families of solitons. Recently, it was shown that for multi-dimensional systems, these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reﬂection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schrödinger equation in such a scenario of partiallyPT-symmetric potential.
A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels
DEFF Research Database (Denmark)
Galeazzi, Roberto; Perez, Tristan
2011-01-01
This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...... to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves – propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion...
Energy Technology Data Exchange (ETDEWEB)
Ryashko, Lev [Ural Federal University, Lenina, 51, Ekaterinburg, 620000 (Russian Federation)
2015-11-30
A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Directory of Open Access Journals (Sweden)
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials.
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Günter, Peter
2008-03-28
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-{3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene} malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites.
Renilson, Martin
2015-01-01
This book adopts a practical approach and presents recent research together with applications in real submarine design and operation. Topics covered include hydrostatics, manoeuvring, resistance and propulsion of submarines. The author briefly reviews basic concepts in ship hydrodynamics and goes on to show how they are applied to submarines, including a look at the use of physical model experiments. The issues associated with manoeuvring in both the horizontal and vertical planes are explained, and readers will discover suggested criteria for stability, along with rudder and hydroplane effectiveness. The book includes a section on appendage design which includes information on sail design, different arrangements of bow planes and alternative stern configurations. Other themes explored in this book include hydro-acoustic performance, the components of resistance and the effect of hull shape. Readers will value the author’s applied experience as well as the empirical expressions that are presented for use a...
Directory of Open Access Journals (Sweden)
V. N. Akimov
2017-01-01
Full Text Available One of the important problems of the designing of maneuverable unmanned aerial vehicles (UAV is to ensure aeroelastic stability with automatic control system (ACS. One of the possible types of aeroelastic instability of UAV with ACS is loss of stability in the system "surface control – actuator". A nonlinear model for the study of the stability of the system "surface control – actuator" is designed for solving problems of joint design of airframe and ACS with the requirements of aeroelasticity. The electric actuator is currently the most widely used on highly maneuverable UAV. The wide bandwidth and the availability of frequency characteristic lifts are typical for the modern electric actuator. This exacerbates the problem of providing aeroelastic stability of the UAV with ACS, including the problem of ensuring the stability of the system "surface control – actuator". In proposed model the surface control, performing bending-torsion oscillations in aerodynamic flow, in fact, is the loading for the actuator. Experimental frequency characteristics of the isolated actuator, obtained for different levels of the control signal, are used for the mathematical description of the actuator, then, as dynamic hinge moment, which is determined by aeroelastic vibrations of the surface control in the air flow, is calculated. Investigation of the stability of the system "surface control – actuator" is carried out by frequency method using frequency characteristics of the open-loop system. The undeniable advantage of the proposed model is the simplicity of obtaining the transfer functions of the isolated actuator. The experiment by its definition is a standard method of determining frequency characteristics of the actuator in contrast to time-consuming experiments for determining the dynamic stiffness of the actuator (with the surface control or the transfer function of the actuator using electromechanical simulation of aeroelastic loading of the
Ottander, John A.; Hall, Robert A.; Powers, J. F.
2018-01-01
A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.
Nonlinear and subharmonic stability analysis in film-driven morphological patterns
Bertagni, Matteo Bernard; Camporeale, Carlo
2017-11-01
The interaction of a gravity-driven water film with an evolving solid substrate (calcite or ice) results in the formation of fascinating wavy patterns similar both in caves and in ice-falls. Due to their remarkable similarity, we adopt a unified approach in the study of pattern formation of longitudinally oriented organ-pipe-like structures, called flutings. Since the morphogenesis of cave patterns can evolve for millennia, they have an additional value as silent repositories of past climates. Fluting formation is studied with the aid of gradient expansion and center manifold projection. In particular, through gradient expansion, a Benney-type equation accounting for the movable boundary is obtained. The coupling with a wall evolution equation provides a morphodynamic model for fluting formation, explored through linear and nonlinear analyses. In this way, closed relationships for the selected wave number and for the finite amplitude are achieved. However, as finite-amplitude monochromatic waves may be destabilized by nonlinear interactions with other modes, we verify, through center manifold projection, the stability of the fundamental to subharmonic disturbances. Conclusively, we perform numerical simulations of the fully nonlinear equations to validate the theory results.
Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy
Xia, Minglu; Sun, Qingping
2017-10-01
Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2016-06-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Large thermally induced nonlinear refraction of gold nanoparticles stabilized by cyclohexanone
Energy Technology Data Exchange (ETDEWEB)
Sarkhosh, Leila; Aleali, Hoda; Karimzadeh, Rouhollah; Mansour, Nastaran [Physics Department, Shahid Beheshti University, Evin 19839, Tehran (Iran, Islamic Republic of)
2010-10-15
Stabilized gold nanoparticle (AuNP) colloids have been fabricated by nanosecond pulsed laser ablation of a pure gold plate in cyclohexanone. The AuNPs colloid exhibits a UV-Vis absorption spectrum with a surface plasmon absorption peak at about 540 nm. Scanning electron microscopy has shown the formation of spherical AuNPs with average size about 53 nm. The shift of 24 cm{sup -1} is observed in the carbonyl band of the colloid using FTIR spectroscopy. This shift indicates that the monomer carbonyl group of cyclohexanone interacts with the surface of the AuNPs and leads to stabilizing the colloid. A large nonlinear refractive index of -2.92 x 10{sup -7} cm{sup 2}/W is measured using the Z-scan technique under continuous wave laser irradiation at 532 nm. Our results show that the large induced nonlinear refraction is attributed to the surface plasmon resonance (SPR) enhancement effect of AuNPs, high thermo-optic coefficient and low thermal conductivity of cyclohexanone. Observation of far-field diffraction ring patterns confirm a thermally induced negative lens effect and spatial self-phase modulation in the laser beam as it traverses the colloids. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control
Directory of Open Access Journals (Sweden)
Chun-xia Dou
2011-01-01
Full Text Available A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribed H∞ disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI technique, some sufficient conditions for the existence of H∞ robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimized H∞ performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.
On the stability and compressive nonlinearity of a physiologically based model of the cochlea
Energy Technology Data Exchange (ETDEWEB)
Nankali, Amir [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Grosh, Karl [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. A positive feedback mechanism within the cochlea, called the cochlear amplifier, provides amplitude and frequency selectivity in the mammalian auditory system. The cochlear amplifier and stability are studied using a nonlinear, micromechanical model of the Organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. It is observed that the mechano-electrical transduction (MET) sensitivity and somatic motility of the outer hair cell (OHC), control the cochlear stability. Increasing MET sensitivity beyond a critical value, while electromechanical coupling coefficient is within a specific range, causes instability. We show that instability in this model is generated through a supercritical Hopf bifurcation. A reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamics is significant while the radial mode can be simplified from the equations. The cochlear amplifier in this model exhibits good agreement with the experimental data. A comprehensive 3-dimensional model based on the cross sectional model is simulated and the results are compared. It is indicated that the global model qualitatively inherits some characteristics of the local model, but the longitudinal coupling along the cochlea shifts the stability boundary (i.e., Hopf bifurcation point) and enhances stability.
Frye, Michael Takaichi
This dissertation examines the problem of global decentralized control by output feedback for large-scale uncertain nonlinear systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. Several innovative techniques will be developed to create decentralized output feedback controllers rendering the closed-loop systems globally asymptotically stable. This is accomplished by extending an output feedback domination design that requires only limited information about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. A time-varying output feedback controller is also constructed for use with large-scale systems that have unknown parameters. Furthermore, a mixed large-scale system consisting of both lower and upper triangular systems is shown to be stabilizable by employing a combined high and low gain domination technique. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. In addition, a new design technique was developed using homogeneous system theory, which allows for the design of nonsmooth controllers and observers to stabilize a class of feedforward system with uncontrollable and unobservable linearization. An example of a large-scale system is a group of autonomous airships performing the function of a temporary mobile cell phone network. An airship mobile cell phone network is a novel solution to the problem of maintaining communication during the advent of extensive damage to the communication infrastructure; be it from a flood, earthquake, hurricane, or terrorist attack. A first principle force-based dynamic model for the Tri-Turbofan Airship was developed and will be discussed in detail. The mathematical model was based on actual flight test data that has been collected at the Gait Analysis and Innovative Technologies Laboratory. This model was developed to research autonomous airship
Improving stability and strength characteristics of framed structures with nonlinear behavior
Pezeshk, Shahram
1990-01-01
In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt
Energy Technology Data Exchange (ETDEWEB)
Alvarez R, J.T
1998-10-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ({sup 4} He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator {rho}hut{sub FP} that is evaluated as Wigneris function through {rho}{sub CG} obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D{sub mn} defined with a nonequilibrium coarse grained statistical operator {rho}hut{sub CG}, matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine {rho}hut{sub CG} by means of the local equilibrium statistical operator {rho}hut{sub l}-tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D{sub mn} but with aid of a quasi equilibrium statistical operator {rho}hut{sub qe} instead
Cho, Yonggeun
2016-05-04
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
International Nuclear Information System (INIS)
Ayten, B.; Westerhof, E.
2014-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al (1989 Phys. Rev. Lett. 62 426). We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker–Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in the case of locked islands or when the magnetic island rotation period is longer than the collisional time scale. The non-linear effects result in an overall reduction of the current drive efficiency for this case with absorption of the EC power on the low-field side of the electron cyclotron resonance layer. As a consequence of the non-linear effects, also the stabilizing effect of the ECCD on the island is reduced from linear expectations. (paper)
Schuller, F. T.
1975-01-01
Hydrodynamic journal stability tests were conducted with tilted-lobe bearings. The bearings had three, five, and seven lobes and length to diameter (L/D) ratios from 0.2 to 1.0. They were tested in water and MIL-L-7808G oil at 294 K (70 F) at speeds to 5400 rpm with zero load. Stability was not appreciably affected by the number of lobes and decreased with a decrease in L/D ratio. However, a three-tilted-lobe bearing with an offset factor of 0.76 and an L/D of 0.5 was more stable than a three centrally lobed bearing with an offset factor of 0.50 and an L/D of 1.0.
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces
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Mohammad Maleki V.
2018-02-01
Full Text Available In this paper, we prove the generalized nonlinear stability of the first and second of the following ρ -functional equations, G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | = ρ ( 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | , and 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | = ρ G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | in latticetic random Banach lattice spaces, where ρ is a fixed real or complex number with ρ ≠ 1 .
Third-order resonance effects and the nonlinear stability of drop oscillations
Natarajan, Ramesh; Brown, Robert A.
1987-01-01
The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small nonaxisymmetric perturbations, as is demonstrated here for the three- and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, nonaxisymmetric traveling-wave solutions are also obtained and their stability is investigated. A nongeneric cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.
On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field
Xu, Lanxi; Lan, Wanli
2017-12-01
Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M, where M is the maximum of the absolute value of the velocity field of the laminar flow.
Grants, Ilmars; Gerbeth, Gunter
2010-07-01
The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by a rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilize the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. These rolls can only be excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this nonlinear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and nonlinear components of this transition by direct numerical simulation of the flow response to noise. It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.
Stability of orbits in nonlinear mechanics for finite but very long times
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab
Stability of orbits in nonlinear mechanics for finite but very long times
Energy Technology Data Exchange (ETDEWEB)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
International Nuclear Information System (INIS)
Itasse, Maxime; Brazier, Jean-Philippe; Léon, Olivier; Casalis, Grégoire
2015-01-01
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m 1 , n 1 ), (m 2 , n 2 ), such that the difference in azimuth and in frequency matches the desired “target” mode (m 1 − m 2 , n 1 − n 2 ). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)
2015-08-15
Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.
Ghodousi, Maryam; Shahgholi, Majid; Payganeh, Gholamhassan
2018-03-01
The objective of the present work is to investigate the nonlinear vibrations of the rotating asymmetrical nano-shafts by considering surface effect. In order to compute the surface stress tensor, the surface elasticity theory is used. The governing nonlinear equations of motion are obtained with the aid of variational approach. Bubnov-Galerkin is a very effective method for exploiting the reduced-order model of the equations of motion. The averaging method is employed to analyze the reduced-order model of the system. For this purpose, the well-known Van der Pol transformation in the complex form and angle-action transformation are utilized. The effect of surface stress on the forward and backward speeds, steady state responses of the system, fixed points, close orbits and stability of the solutions is examined. The preliminary results of the research show that the absolute values of forward and backward whirling speeds in the presence of surface effect with positive residual surface stress are higher than those of regarding the system without surface effect and in the presence of surface effect with negative residual surface stress. In addition, it is seen that the undamped rotating asymmetrical nano-shaft, for specified value of detuning parameter, in the absence or presence of surface effect has various number of stable and unstable periodic solutions. Besides, there is different number of separatrix (homoclinic orbit type). Furthermore, bifurcations, number of solutions and their stability for damped rotating asymmetrical nano-shaft are investigated. Also, the above results have been obtained for rotating symmetrical nano-shaft.
A nonlinear optimal control approach to stabilization of a macroeconomic development model
Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.
2017-11-01
A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.
Ni, Junkang; Liu, Chongxin; Liu, Hang
2017-01-01
This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme.
Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent
2011-05-01
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neuman...
Directory of Open Access Journals (Sweden)
Philippe eTerrier
2013-09-01
Full Text Available It has been observed that times series of gait parameters (stride length (SL, stride time (ST and stride speed (SS, exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another nonlinear method estimates the degree of resilience of gait control to small perturbations, i.e. the local dynamic stability (LDS. The method makes use of the maximal Lyapunov exponent, which estimates how fast a nonlinear system embedded in a reconstructed state space (attractor diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST and SS from which the statistical persistence among consecutive strides can be assessed, and the trajectory of the center of pressure (from which the LDS can be estimated. In 20 healthy participants, the response to rhythmic auditory cueing (RAC of LDS and of statistical persistence (assessed with detrended fluctuation analysis (DFA was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor was strongly enhanced (relative change +47%. That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step was smaller (+3%. DFA results (scaling exponents confirmed an anti-persistent pattern in ST, SL and SS. Long-term LDS (but not short-term LDS and scaling exponents exhibited a significant correlation between them (r=0.7. Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders.
International Nuclear Information System (INIS)
R Paul Drake
2004-01-01
OAK-B135 This is the final report from the project Hydrodynamics by High-Energy-Density Plasma Flow and Hydrodynamics and Radiation Hydrodynamics with Astrophysical Applications. This project supported a group at the University of Michigan in the invention, design, performance, and analysis of experiments using high-energy-density research facilities. The experiments explored compressible nonlinear hydrodynamics, in particular at decelerating interfaces, and the radiation hydrodynamics of strong shock waves. It has application to supernovae, astrophysical jets, shock-cloud interactions, and radiative shock waves
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2017-12-01
In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-01-01
Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
Lu, Junjie; She, Zhikun
2016-11-01
In this paper, we investigate sufficient and necessary conditions of uniform local exponential stability (ULES) for the discrete-time nonlinear switched system (DTNSS). We start with the definition of T-step common Lyapunov functions (CLFs), which is a relaxation of traditional CLFs. Then, for a time-varying DTNSS, by constructing such a T-step CLF, a necessary and sufficient condition for its ULES is provided. Afterwards, we strengthen it based on a T-step Lipschitz continuous CLF. Especially, when the system is time-invariant, by the smooth approximation theorem, the Lipschitz continuity condition of T-step CLFs can further be replaced by continuous differentiability; and when the system is time-invariant and homogeneous, due to the extension of Weierstrass approximation theorem, T-step continuously differentiable CLFs can even be strengthened to be T-step polynomial CLFs. Furthermore, three illustrative examples are additionally used to explain our main contribution. In the end, an equivalence between time-varying DTNSSs and their corresponding linearisations is discussed.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Gottlieb, Sigal
2015-04-10
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.
Michiels, Wim; Nijmeijer, Henk
2009-09-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties
Directory of Open Access Journals (Sweden)
Ruofeng Rao
2013-01-01
Full Text Available The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω, Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.
Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.
2018-04-01
We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.
Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping
2014-11-01
In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Miao, Hui; Teng, Zhidong; Li, Zhiming
2016-01-01
The dynamical behaviors for a five-dimensional viral infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses, and nonlinear incidence rate are investigated. The threshold values for viral infection, antibody response, CTL immune response, CTL immune competition, and antibody competition, respectively, are established. Under certain assumptions, the threshold value conditions on the global stability of the infection-free, im...
Posbergh, T. A.; Simo, J. C.; Marsden, J. E.
1989-01-01
This paper applies the energy-momentum method to the problem of nonlinear stability of relative equilibria of a rigid body with attached flexible appendage in a uniformly rotating state. The appendage is modeled as a geometrically exact rod which allows for finite bending, shearing and twist in three dimensions. Application of the energy-momentum method to this example depends crucially on a special choice of variables in terms of which the second variation block diagonalizes into blocks a...
Stability, diffusion and interactions of nonlinear excitations in a many body system
Coste, Christophe; Jean, Michel Saint; Dessup, Tommy
2017-04-01
When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.
Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; van de Looij, Ruud; Thomsen, Jon Juel
2014-01-01
This work experimentally investigates the impact of nonlinearity on macromechanical parametric amplification. For a strong cubic stiffness nonlinearity we observe jumps in gain (ratio of steady-state vibration amplitude of the externally and parametrically excited system, to vibration amplitude o...
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Wang, J.; Xu, K.; Restreppo, G. A.; Bentley, S. J.; Meng, X.; Zhang, X.
2017-12-01
Due to global sea level rise, local subsidence and sediment deficit, the Mississippi River (MR) deltaic plain has lost a total of 25% of coastal Louisiana's wetlands during the last century, leading to huge losses of ecological services, economic and social crises. Ecosystem-based restoration strategies which rely on coastal system processes and feedbacks are urgently needed. Understanding linkages between estuarine and coastal systems and the adjacent marshlands will help the designing strategies. To investigate bay hydrodynamics and its impacts on the adjacent micro-tidal wetland stability, hourly measurements of wave, tidal current, and benthic sediment concentration in summer, winter, and spring of 2015-2016 were conducted in Fourleague Bay, Louisiana, USA. The bay-marsh system has been stable for almost 80 years under high relative sea level rising rate, which is 11 km southeast of the Atchafalaya River mouth, with a water depth of 1-3 m. High-temporal resolution data indicate that benthic sediment resuspension is mainly caused by wind-driven waves with a dominant periodicity of 4.8 d. The sediment flux reaches 28 g·m-1·s-1 per unit depth in cm during the events. Net sediment transport is northwestward in summer, and southeastward in winter and spring. Sediment flux available for surrounding marsh varies from 0-500 g·m-1·s-1. An optimal inundation depth of 50 cm is estimated by the equilibrium wetland elevation change model under high relative sea level rising rate of 1.57 cm·yr-1. Seasonal variations of river discharge and wind direction (particularly speeds >3 m·s-1) greatly impact potential sediment contribution from bay to the surrounding wetlands. Three sediment transport regimes are concluded based on the seasonal variations of river discharge and wind direction: the `bypassing' season, the resuspension-accumulation season, and the combined `bypassing' and resuspension-accumulation season. The bay hydrodynamic processes and their impacts on the
Stability and suppression of turbulence in relaxing molecular gas flows
Grigoryev, Yurii N
2017-01-01
This book presents an in-depth systematic investigation of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The work describes the theoretical foundations of a new way to control stability and laminar turbulent transitions in aerodynamic flows. It develops hydrodynamic models for describing thermal nonequilibrium gas flows which allow the consideration of suppression of inviscid acoustic waves in 2D shear flows. Then, nonlinear evolution of large-scale vortices and Kelvin-Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both linear and nonlinear classical energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of the book is to show the new dissipative effect, which can be used for flo...
Thermally stimulated nonlinear refraction in gelatin stabilized Cu-PVP nanocomposite thin films
Energy Technology Data Exchange (ETDEWEB)
Tamgadge, Y. S., E-mail: ystamgadge@gmail.com; Atkare, D. V. [Department of Physics, Mahatma Fule Arts, Commerce & SitaramjiChoudhari Science College, Warud, Dist. Amravati (MS), India-444906 (India); Pahurkar, V. G.; Muley, G. G., E-mail: gajananggm@yahoo.co.in [Department of Physics, SantGadge Baba Amravati University, Amravati (MS), India-444602 (India); Talwatkar, S. S. [Department of Physics, D K Marathe and N G Acharya College, Chembur, Mumbai (MS), India-440071 (India); Sunatkari, A. L. [Department of Physics, Siddharth College of Arts, Science and Commerce, Fort, Mumbai (MS), India-440001 (India)
2016-05-06
This article illustrates investigations on thermally stimulated third order nonlinear refraction of Cu-PVP nanocomposite thin films. Cu nanoparticles have been synthesized using chemical reduction method and thin films in PVP matrix have been obtained using spin coating technique. Thin films have been characterized by X-ray diffraction (XRD) and Ultraviolet-visible (UV-vis) spectroscopyfor structural and linear optical studies. Third order nonlinear refraction studies have been performed using closed aperture z-scan technique under continuous wave (CW) He-Ne laser. Cu-PVP nanocomposites are found to exhibit strong nonlinear refractive index stimulated by thermal lensing effect.
Directory of Open Access Journals (Sweden)
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Bonneau, Dominique; Souchet, Dominique
2014-01-01
This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the rheological models and the equations of lubrication. It also presents the numerical approaches used to solve the above equations by finite differences, finite volumes and finite elements methods.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 9. Hydrodynamic Lubrication Experiment with 'Floating' Drops. Jaywant H Arakeri K R Sreenivas. General Article Volume 1 Issue 9 September 1996 pp 51-58. Fulltext. Click here to view fulltext PDF. Permanent link:
Energy Technology Data Exchange (ETDEWEB)
Bulatov, A.I.; Chernov, V.S.; Prokopov, L.I.; Proselkov, Yu.M.; Tikhonov, Yu.P.
1980-01-15
A hydrodynamic disperser is suggested which contains a housing, slit nozzles installed on a circular base arranged opposite from each other, resonators secured opposite the nozzle and outlet sleeve. In order to improve the effectiveness of dispersion by throttling the flow, each resonator is made in the form of a crimped plate with crimpings that decrease in height in a direction towards the nozzle.
Milne-Thomson, L M
2011-01-01
This classic exposition of the mathematical theory of fluid motion is applicable to both hydrodynamics and aerodynamics. Based on vector methods and notation with their natural consequence in two dimensions - the complex variable - it offers more than 600 exercises and nearly 400 diagrams. Prerequisites include a knowledge of elementary calculus. 1968 edition.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
Smith, L. L.; Morino, L.
1975-01-01
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
Zheligovsky, Vladislav
2011-01-01
New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.
DEFF Research Database (Denmark)
Hansen, Jesper Schmidt; Dyre, Jeppe C.; Daivis, Peter J.
2011-01-01
We show by nonequilibrium molecular dynamics simulations that the Navier-Stokes equation does not correctly describe water flow in a nanoscale geometry. It is argued that this failure reflects the fact that the coupling between the intrinsic rotational and translational degrees of freedom becomes...... important for nanoflows. The coupling is correctly accounted for by the extended Navier-Stokes equations that include the intrinsic angular momentum as an independent hydrodynamic degree of freedom. © 2011 American Physical Society....
Prakash, T.; Singha, M. K.; Ganapathi, M.
2009-02-01
Nonlinear behavior of functionally graded material (FGM) skew plates under in-plane load is investigated here using a shear deformable finite element method. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the first order shear deformation theory based on exact neutral surface position is employed here. The present model is compared with the conventional mid-surface based formulation, which uses extension-bending coupling matrix to include the noncoincidence of neutral surface with the geometric mid-surface for unsymmetric plates. The nonlinear governing equations are solved through Newton Raphson technique. The nonlinear behavior of FGM skew plates under compressive and tensile in-plane load are examined considering different system parameters such as constituent gradient index, boundary condition, thickness-to-span ratio and skew angle.
Hydrodynamics of oceans and atmospheres
Eckart, Carl
1960-01-01
Hydrodynamics of Oceans and Atmospheres is a systematic account of the hydrodynamics of oceans and atmospheres. Topics covered range from the thermodynamic functions of an ideal gas and the thermodynamic coefficients for water to steady motions, the isothermal atmosphere, the thermocline, and the thermosphere. Perturbation equations, field equations, residual equations, and a general theory of rays are also presented. This book is comprised of 17 chapters and begins with an introduction to the basic equations and their solutions, with the aim of illustrating the laws of dynamics. The nonlinear
Nonlinear power flow feedback control for improved stability and performance of airfoil sections
Wilson, David G.; Robinett, III, Rush D.
2013-09-03
A computer-implemented method of determining the pitch stability of an airfoil system, comprising using a computer to numerically integrate a differential equation of motion that includes terms describing PID controller action. In one model, the differential equation characterizes the time-dependent response of the airfoil's pitch angle, .alpha.. The computer model calculates limit-cycles of the model, which represent the stability boundaries of the airfoil system. Once the stability boundary is known, feedback control can be implemented, by using, for example, a PID controller to control a feedback actuator. The method allows the PID controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be optimized. This permits operation closer to the stability boundaries, while preventing the physical apparatus from unintentionally crossing the stability boundaries. Operating closer to the stability boundaries permits greater power efficiencies to be extracted from the airfoil system.
Nonlinear stability of m=1 flute mode in a nonparaxial open plasma device
International Nuclear Information System (INIS)
Lanskij, I.M.; Stupakov, G.V.
1991-01-01
Plasma flute stability as to high shifts under strong effects of ion Larmor finite radius conditions is studied. System consisting of long axisymmetric paraxial mirror device with stabilizing cells at its edges is considered. Variation of plasma energy as to its shift as a whole is calculated. It is shown, that depending on stabilizer type the force bringing plasma back in equilibrium state with shift growth may both increase and decrease
Directory of Open Access Journals (Sweden)
Hamid Reza Karimi
2009-01-01
Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.
The Korteweg-de Vries soliton in the lattice hydrodynamic model
Ge, H. X.
2009-04-01
The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.
Directory of Open Access Journals (Sweden)
J. Gwinner
2013-01-01
Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.
Directory of Open Access Journals (Sweden)
Jónas Elíasson
2014-01-01
Full Text Available A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls. The method shows how many modes are unstable, the wave number instability band within each mode, the maximum growth rate (most critical wave numbers on each mode, and the nonlinear growth rates for each amplitude as a function of the porous Rayleigh number. Single amplitude controls the nonlinear growth rates and thereby the physical flow rate and fluid velocity, on each mode. They are called the flak amplitudes. A discrete Fourier transform is used for numerical simulations and here frequency combinations appear that the traditional cut-off infinite transforms do not have. The discrete show a stationary solution in the weak instability phase, but when carried past 2 unstable modes they show fluctuating motion where all amplitudes except the flak may be zero on the average. This leads to a flak amplitude scaling process of the heat conduction, producing an eddy heat conduction coefficient where a Nu-RaL relationship is found. It fits better to experiments than previously found solutions but is lower than experiments.
International Nuclear Information System (INIS)
Hennig, D.
1997-01-01
In boiling water reactors, there is a region in the operating map for which the reactor exhibits stable or unstable power oscillations. This oscillatory behaviour had to be understood in detail, in order to estimate, in a reliable way, the stability limits. This paper describes the BWR stability analysis methodology used at PSI and presents some recent results. (author) figs., tab., 38 refs
Directory of Open Access Journals (Sweden)
Olav Slupphaug
1999-07-01
Full Text Available In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.
Robinett III, Rush D
2011-01-01
Nonlinear Powerflow Control Design presents an innovative control system design process motivated by renewable energy electric grid integration problems. The concepts developed result from the convergence of three research and development goals: • to create a unifying metric to compare the value of different energy sources – coal-burning power plant, wind turbines, solar photovoltaics, etc. – to be integrated into the electric power grid and to replace the typical metric of costs/profit; • to develop a new nonlinear control tool that applies power flow control, thermodynamics, and complex adaptive systems theory to the energy grid in a consistent way; and • to apply collective robotics theories to the creation of high-performance teams of people and key individuals in order to account for human factors in controlling and selling power into a distributed, decentralized electric power grid. All three of these goals have important concepts in common: exergy flow, limit cycles, and balance between compe...
DEFF Research Database (Denmark)
Yao, Wei; Fang, Jiakun; Zhao, Ping
2013-01-01
the characteristics of the conventional PID, but adjust the parameters of PID controller online using identified Jacobian information from RBFNN. Hence, it has strong adaptability to the variation of the system operating condition. The effectiveness of the proposed controller is tested on a two-machine five-bus power......In this paper, a nonlinear adaptive damping controller based on radial basis function neural network (RBFNN), which can infinitely approximate to nonlinear system, is proposed for thyristor controlled series capacitor (TCSC). The proposed TCSC adaptive damping controller can not only have...... system and a four-machine two-area power system under different operating conditions in comparison with the lead-lag damping controller tuned by evolutionary algorithm (EA). Simulation results show that the proposed damping controller achieves good robust performance for damping the low frequency...
Global stability of a network-based SIS epidemic model with a general nonlinear incidence rate.
Huang, Shouying; Jiang, Jifa
2016-08-01
In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold R0 which completely governs the disease dynamics: when R0 1, the disease is permanent. It is interesting that the threshold value R0 bears no relation to the functional form of the nonlinear incidence rate and degree-dependent birth. Furthermore, by applying an iteration scheme and the theory of cooperative system respectively, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. Our results improve and generalize some known results. To illustrate the theoretical results, the corresponding numerical simulations are also given.
Linear and non-linear control of wind farms. Contribution to the grid stability
Energy Technology Data Exchange (ETDEWEB)
Fernandez, R.D. [Laboratorio de Electronica, Facultad de Ingenieria, Universidad Nacional de la Patagonia San Juan Bosco, Ciudad Universitaria, Km. 4, 9000, Comodoro Rivadavia (Argentina); Mantz, R.J. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina); Comision de Investigaciones Cientificas de la Provincia de Buenos Aires, CICpBA, La Plata (Argentina); Battaiotto, P.E. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina)
2010-06-15
This paper deals with linear and non-linear control of wind farms equipped with doubly-fed induction generators (DFIG). Both, active and reactive wind farm powers are employed in two independent control laws in order to increase the damping of the oscillation modes of a power system. In this way, it presented a general strategy where two correction terms are added, one by each independent control, to the normal operating condition of a wind farm. The proposed control laws are derived from the Lyapunov approach. Meanwhile for the reactive power a non-linear correction is presented, for the wind farm active power it is demonstrated that the classical proportional and inertial laws can be considered via the Lyapunov approach if wind farms are considered as real power plants, i.e. equivalent to conventional synchronous generation. Finally, some simulations are presented in order to support the theoretical considerations demonstrating the potential contributions of both control laws. (author)
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
scale dynamics systems. Perhaps the most far reaching impact of this DRI will be a contribution that was not planned in the original proposal. This... contribution has to do with the generalization of Koopman decompositions using a fractional calculus perspective on complexity. By using a combination of... influenced by an external environment in which long-term memory is introduced. 15. SUBJECT TERMS nonlinear dynamics, spectral decompositions, fractional
Stability of nonlinear Hamiltonian motion for a finite but very long time
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1991-01-01
By constructing action variables that are very nearly invariant in a region Ω of phase space, and by examining their residual variation, we set long-term bounds on any orbit starting in an open subregion of Ω. A new and generally applicable method for constructing the required high-precision invariants is applied. The technique is illustrated for transverse oscillations in a circular accelerator, a case with 21/2 degrees of freedom and strong nonlinearity
Quantum Plasmas An Hydrodynamic Approach
Haas, Fernando
2011-01-01
This book provides an overview of the basic concepts and new methods in the emerging scientific area known as quantum plasmas. In the near future, quantum effects in plasmas will be unavoidable, particularly in high density scenarios such as those in the next-generation intense laser-solid density plasma experiment or in compact astrophysics objects. Currently, plasmas are in the forefront of many intriguing questions around the transition from microscopic to macroscopic modeling of charged particle systems. Quantum Plasmas: an Hydrodynamic Approach is devoted to the quantum hydrodynamic model paradigm, which, unlike straight quantum kinetic theory, is much more amenable to investigate the nonlinear realm of quantum plasmas. The reader will have a step-by-step construction of the quantum hydrodynamic method applied to plasmas. The book is intended for specialists in classical plasma physics interested in methods of quantum plasma theory, as well as scientists interested in common aspects of two major areas of...
Globally Asymptotic Stability of Stochastic Nonlinear Systems by the Output Feedback
Directory of Open Access Journals (Sweden)
Wenwen Cheng
2015-01-01
the traditional mathematical induction method. Indeed, we develop a new method to study the globally asymptotic stability by introducing a series of specific inequalities. Moreover, an example and its simulations are given to illustrate the theoretical result.
Laser driven hydrodynamic instability experiments
International Nuclear Information System (INIS)
Remington, B.A.; Weber, S.V.; Haan, S.W.; Kilkenny, J.D.; Glendinning, S.G.; Wallace, R.J.; Goldstein, W.H.; Wilson, B.G.; Nash, J.K.
1993-01-01
An extensive series of experiments has been conducted on the Nova laser to measure hydrodynamic instabilities in planar foils accelerated by x-ray ablation. Single mode experiments allow a measurement of the fundamental growth rates from the linear well into the nonlinear regime. Two-mode foils allow a first direct observation of mode coupling. Surface-finish experiments allow a measurement of the evolution of a broad spectrum of random initial modes
Small-Scale Magnetic Helicity and Nonlinear Stabilization of the Dynamo
Sokoloff, D. D.; Yushkov, E. V.; Lukin, A. S.
2017-12-01
According to present-day ideas, nonlinear saturation of the astrophysical dynamo and, in particular, the solar dynamo, are based on the consideration of the magnetic helicity balance, to which the helicities of the large-scale magnetic field and small-scale field related to it contributed. We show that, in a mirrorasymmetric medium, the small-scale magnetic field generated by the small-scale dynamo also has a nonzero magnetic helicity, which also should be taken into account in the magnetic helicity balance.
Stabilization of the solution of a doubly nonlinear parabolic equation
International Nuclear Information System (INIS)
Andriyanova, È R; Mukminov, F Kh
2013-01-01
The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x→∞ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles
Constantoudis, Vassilios; Nicolaides, Cleanthes A
2005-02-22
The dissociation dynamics of a dichromatically laser-driven diatomic Morse molecule vibrating in the ground state is investigated by applying tools of the nonlinear theory of classical Hamiltonian systems. Emphasis is placed on the role of the relative phase of the two fields, phi. First, it is found that, just like in quantum mechanics, there is dependence of the dissociation probability on phi. Then, it is demonstrated that addition of the second laser leads to suppression of probability (stabilization), when the intensity of the first laser is kept constant just above or below the single laser dissociation threshold. This "chemical bond hardening" diminishes as phi increases. These effects are investigated and interpreted in terms of modifications in phase space topology. Variations of phi as well as of the intensity of the second laser may cause (i) appearance/disappearance of the stability island corresponding to the common resonance with the lowest energy and (ii) deformation and movement of the region of Kolmogorov-Arnold-Moser tori that survive from the undriven system. The latter is the main origin in phase space of stabilization and phi dependence. Finally, it is shown that the use of short laser pulses enhances both effects.
International Nuclear Information System (INIS)
Colgate, S.A.
1981-01-01
The explosion of a star supernova occurs at the end of its evolution when the nuclear fuel in its core is almost, or completely, consumed. The star may explode due to a small residual thermonuclear detonation, type I SN or it may collapse, type I and type II SN leaving a neutron star remnant. The type I progenitor should be thought to be an old accreting white dwarf, 1.4 M/sub theta/, with a close companion star. A type II SN is thought to be a massive young star 6 to 10 M/sub theta/. The mechanism of explosion is still a challenge to our ability to model the most extreme conditions of matter and hydrodynamics that occur presently and excessively in the universe. 39 references
Energy Technology Data Exchange (ETDEWEB)
Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it [Department of Chemistry, Biology and Biotechnology, University of Perugia, 06123 Perugia (Italy); Gotoda, Hiroshi [Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu-shi, Shiga 525-8577 (Japan); Dolnik, Milos; Epstein, Irving R. [Department of Chemistry, Brandeis University, Waltham, Massachusetts 02454-9110 (United States)
2015-01-15
Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.
Gentili, Pier Luigi; Gotoda, Hiroshi; Dolnik, Milos; Epstein, Irving R
2015-01-01
Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.
Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity
Rand, J. L.; Wakefield, D. S.
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may
Hydrodynamic approach to electronic transport in graphene
Energy Technology Data Exchange (ETDEWEB)
Narozhny, Boris N. [Institute for Theoretical Condensed Matter Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Gornyi, Igor V. [Institute for Theoretical Condensed Matter Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany); Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe (Germany); Ioffe Physical Technical Institute, St. Petersburg (Russian Federation); Mirlin, Alexander D. [Institute for Theoretical Condensed Matter Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany); Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe (Germany); Petersburg Nuclear Physics Institute, St. Petersburg (Russian Federation); Schmalian, Joerg [Institute for Theoretical Condensed Matter Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany); Institute for Solid State Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany)
2017-11-15
The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. In this paper we briefly review the recent advances, both theoretical and experimental, in the hydrodynamic approach to electronic transport in graphene, focusing on viscous phenomena, Coulomb drag, non-local transport measurements, and possibilities for observing nonlinear effects. (copyright 2017 by WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Stability analysis and controller design for a linear system with Duhem hysteresis nonlinearity
Ouyang, Ruiyue; Jayawardhana, Bayu
2012-01-01
In this paper, we investigate the stability of feedback interconnections between a linear system and a Duhem hysteresis operator, where the linear system satisfies either counter-clockwise (CCW) or clockwise (CW) inputoutput dynamics [1], [13]. More precisely, depending on the input-output dynamics
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
Kilpatrick, Zachary P.
2010-06-01
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather. © 2010 Elsevier B.V. All rights reserved.
Stabilization of the higher order nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
18
can describe the propagation of ultrashort light pulses which are shorter than ∼ 10−13s. In practical applications, sometimes we may want to prevent the propagation of some signal in optical fibre, the stabilization of the HNLS equation can be viewed as a good mathematical representation of this phenomenon. To state the ...
Directory of Open Access Journals (Sweden)
Erdal Korkmaz
2017-06-01
Full Text Available Abstract In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov’s second method. The results obtained essentially improve, include and complement the results in the literature.
Korkmaz, Erdal
2017-01-01
In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.
Stabilization of a class of sandwich nonlinear systems via state feedback
Wang, Xu; Stoorvogel, Antonie Arij; Saberi, Ali; Grip, H°avard Fjær; Roy, Sandip; Sannuti, Peddapullaiah
2009-01-01
In this paper, we consider the problems of semi-global and global internal stabilization of a class of sandwich systems consisting of two linear systems with a saturation element in between. We provide necessary and sufficient conditions for solvability of these problems by state feedback, and
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
Thermo-hydrodynamic lubrication in hydrodynamic bearings
Bonneau, Dominique; Souchet, Dominique
2014-01-01
This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.
Maxfield, Lynn; Palaparthi, Anil; Titze, Ingo
2017-03-01
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths. Copyright © 2017 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
Cichalewski, w
2010-01-01
The high power amplifiers transfer characteristics nonlinearities can have a negative influence on the overall system performance. This is also true for the TESLA superconducting cavities accelerating field parameters control systems. This Low Level Radio Frequency control systems uses microwave high power amplifiers (like 10 MW klystrons) as actuators in the mentioned feedback loops. The amplitude compression and phase deviations phenomena introduced to the control signals can reduce the feedback performance and cause electron beam energy instabilities. The transfer characteristics deviations in the Free Electron Laser in Hamburg experiment have been investigated. The outcome of this study together with the description of the developed linearization method based on the digital predistortion approach have been described in this paper. Additionally, the results from the linearization tool performance tests in the FLASH's RF systems have been placed.
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
2011-01-01
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
Observer-Based Stabilization of Spacecraft Rendezvous with Variable Sampling and Sensor Nonlinearity
Directory of Open Access Journals (Sweden)
Zhuoshi Li
2013-01-01
Full Text Available This paper addresses the observer-based control problem of spacecraft rendezvous with nonuniform sampling period. The relative dynamic model is based on the classical Clohessy-Wiltshire equation, and sensor nonlinearity and sampling are considered together in a unified framework. The purpose of this paper is to perform an observer-based controller synthesis by using sampled and saturated output measurements, such that the resulting closed-loop system is exponentially stable. A time-dependent Lyapunov functional is developed which depends on time and the upper bound of the sampling period and also does not grow along the input update times. The controller design problem is solved in terms of the linear matrix inequality method, and the obtained results are less conservative than using the traditional Lyapunov functionals. Finally, a numerical simulation example is built to show the validity of the developed sampled-data control strategy.
Nonlinear Stochastic stability analysis of Wind Turbine Wings by Monte Carlo Simulations
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Iwankiewiczb, R.; Nielsen, Søren R.K.
2007-01-01
and inertial contributions. A reduced two-degrees-of-freedom modal expansion is used specifying the modal coordinate of the fundamental blade and edgewise fixed base eigenmodes of the beam. The rotating beam is subjected to harmonic and narrow-banded support point motion from the nacelle displacement...... under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore......, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations....
Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain
Directory of Open Access Journals (Sweden)
Geir Hovland
2017-10-01
Full Text Available In this paper a novel feedback controller and stability analysis of a blockchain implementation is developed by using a control engineering perspective. The controller output equals the difficulty adjustment in the mining process while the feedback variable is the average block time over a certain time period. The computational power (hash rate of the miners is considered a disturbance in the model. The developed controller is tested against a simulation model with constant disturbance, step and ramp responses as well as with a high-frequency sinusoidal disturbance. Stability and a fast response is demonstrated in all these cases with a controller which adjusts it's output at every new block. Finally the performance of the controller is implemented and demonstrated on a testnet with a constant hash rate as well as on the mainnet of a public open source blockchain project.
International Nuclear Information System (INIS)
Pryce, M.H.L.
1985-01-01
A dominant mechanism contributing to hydrodynamic dispersion in fluid flow through rocks is variation of travel speeds within the channels carrying the fluid, whether these be interstices between grains, in granular rocks, or cracks in fractured crystalline rocks. The complex interconnections of the channels ensure a mixing of those parts of the fluid which travel more slowly and those which travel faster. On a macroscopic scale this can be treated statistically in terms of the distribution of times taken by a particle of fluid to move from one surface of constant hydraulic potential to another, lower, potential. The distributions in the individual channels are such that very long travel times make a very important contribution. Indeed, while the mean travel time is related to distance by a well-defined transport speed, the mean square is effectively infinite. This results in an asymmetrical plume which differs markedly from a gaussian shape. The distribution of microscopic travel times is related to the distribution of apertures in the interstices, or in the microcracks, which in turn are affected in a complex way by the stresses acting on the rock matrix
Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.
2018-03-01
In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.
Numerical study of solitary wave stability in cubic nonlinear Dirac equations in 1D
Lakoba, T. I.
2018-02-01
Recently there has occurred a controversy between the semi-analytical prediction of linear stability of the soliton of the massive Gross-Neveu model and direct numerical observations of its instability for small values of the frequency. We revisit the problem of numerical computation of this soliton, find a mechanism behind the numerical instability observed in earlier studies, and propose methods to stably compute the soliton over long times. Thus, we confirm the semi-analytical prediction of the soliton's being linearly stable.
Stability, Bifurcation, and Chaos in N-Firm Nonlinear Cournot Games
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2011-01-01
Full Text Available An N-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in which N is divided into two groups and the other in which N is divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly and three-firm (triopoly models to shed light on roles of the number of the firms.
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
Effect of nonlinear energy transport on neoclassical tearing mode stability in tokamak plasmas
Fitzpatrick, Richard
2017-05-01
An investigation is made into the effect of the reduction in anomalous perpendicular electron heat transport inside the separatrix of a magnetic island chain associated with a neoclassical tearing mode in a tokamak plasma, due to the flattening of the electron temperature profile in this region, on the overall stability of the mode. The onset of the neoclassical tearing mode is governed by the ratio of the divergences of the parallel and perpendicular electron heat fluxes in the vicinity of the island chain. By increasing the degree of transport reduction, the onset of the mode, as the divergence ratio is gradually increased, can be made more and more abrupt. Eventually, when the degree of transport reduction passes a certain critical value, the onset of the neoclassical tearing mode becomes discontinuous. In other words, when some critical value of the divergence ratio is reached, there is a sudden bifurcation to a branch of neoclassical tearing mode solutions. Moreover, once this bifurcation has been triggered, the divergence ratio must be reduced by a substantial factor to trigger the inverse bifurcation.
Directory of Open Access Journals (Sweden)
J. Ju
2017-07-01
Full Text Available The flexible Cartesian robotic manipulator (FCRM is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.
Chang, Chau-Lyan
2003-01-01
During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary
Laser driven hydrodynamic instability experiments
International Nuclear Information System (INIS)
Remington, B.A.; Weber, S.V.; Haan, S.W.; Kilkenny, J.D.; Glendinning, S.G.; Wallace, R.J.; Goldstein, W.H.; Wilson, B.G.; Nash, J.K.
1992-01-01
We have conducted an extensive series of experiments on the Nova laser to measure hydrodynamic instabilities in planar foils accelerated by x-ray ablation. Single mode experiments allow a measurement of the fundamental growth rates from the linear well into the nonlinear regime; multimode foils allow an assessment of the degree of mode coupling; and surface-finish experiments allow a measurement of the evolution of a broad spectrum of random initial modes. Experimental results and comparisons with theory and simulations are presented
Makarov, D. V.; Uleysky, M. Yu.
2017-02-01
Binary discrete nonlinear Schrödinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime of strong nonlinearity, a wavepacket corresponding to condensate separates into localized and ballistic fractions. Localized fraction is predominantly formed by immiscible solitons consisted of only one species. Immiscible solitons are formed from initially non-separated states after transient chaotic regime. We calculate the finite-time Lyapunov exponent as a rate of wavepacket divergence in the Hilbert space. Appearance of immiscible solitons to spontaneous self-stabilization of the wavepacket. It is found that onset of chaos is accompanied by fast variations of interaction energy and energy of inter-site tunneling. Crossover to self-stabilization is accompanied by reduction of condensate density due to emittance of ballistically propagating waves.
Kang, An-Ming; Yan, Hong-Sen
2018-02-01
Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Modelling free surface flows with smoothed particle hydrodynamics
Directory of Open Access Journals (Sweden)
L.Di G.Sigalotti
2006-01-01
Full Text Available In this paper the method of Smoothed Particle Hydrodynamics (SPH is extended to include an adaptive density kernel estimation (ADKE procedure. It is shown that for a van der Waals (vdW fluid, this method can be used to deal with free-surface phenomena without difficulties. In particular, arbitrary moving boundaries can be easily handled because surface tension is effectively simulated by the cohesive pressure forces. Moreover, the ADKE method is seen to increase both the accuracy and stability of SPH since it allows the width of the kernel interpolant to vary locally in a way that only the minimum necessary smoothing is applied at and near free surfaces and sharp fluid-fluid interfaces. The method is robust and easy to implement. Examples of its resolving power are given for both the formation of a circular liquid drop under surface tension and the nonlinear oscillation of excited drops.
Directory of Open Access Journals (Sweden)
Jun Dong
2017-07-01
Full Text Available The large-scale penetration of wind power might lead to degradation of the power system stability due to its inherent feature of randomness. Hence, proper control designs which can effectively handle various uncertainties become very crucial. This paper designs a novel robust passive control (RPC scheme of a doubly-fed induction generator (DFIG for power system stability enhancement. The combinatorial effect of generator nonlinearities and parameter uncertainties, unmodelled dynamics, wind speed randomness, is aggregated into a perturbation, which is rapidly estimated by a nonlinear extended state observer (ESO in real-time. Then, the perturbation estimate is fully compensated by a robust passive controller to realize a globally consistent control performance, in which the energy of the closed-loop system is carefully reshaped through output feedback passification, such that a considerable system damping can be injected to improve the transient responses of DFIG in various operation conditions of power systems. Six case studies are carried out while simulation results verify that RPC can rapidly stabilize the disturbed DFIG system much faster with less overshoot, as well as supress power oscillations more effectively compared to that of linear proportional-integral-derivative (PID control and nonlinear feedback linearization control (FLC.
The theoretical analysis of the lattice hydrodynamic models for traffic flow theory
Ge, H. X.; Cheng, R. J.; Lei, L.
2010-07-01
The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.
Hydrodynamic instabilities in miscible fluids
Truzzolillo, Domenico; Cipelletti, Luca
2018-01-01
Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety of forcing conditions. In the absence of a regularizing mechanism, these disturbances would grow indefinitely. For immiscible fluids, interfacial tension provides such a regularizing mechanism, because of the energy cost associated to the creation of new interface by a growing disturbance. For miscible fluids, however, the very existence of interfacial stresses that mimic an effective surface tension is debated. Other mechanisms, however, may also be relevant, such as viscous dissipation. We shall review the stabilizing mechanisms that control the most common hydrodynamic instabilities, highlighting those cases for which the lack of an effective interfacial tension poses deep conceptual problems in the mathematical formulation of a linear stability analysis. Finally, we provide a short overview on the ongoing research on the effective, out of equilibrium interfacial tension between miscible fluids.
Hydrodynamic instabilities in miscible fluids.
Truzzolillo, Domenico; Cipelletti, Luca
2018-01-24
Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety of forcing conditions. In the absence of a regularizing mechanism, these disturbances would grow indefinitely. For immiscible fluids, interfacial tension provides such a regularizing mechanism, because of the energy cost associated to the creation of new interface by a growing disturbance. For miscible fluids, however, the very existence of interfacial stresses that mimic an effective surface tension is debated. Other mechanisms, however, may also be relevant, such as viscous dissipation. We shall review the stabilizing mechanisms that control the most common hydrodynamic instabilities, highlighting those cases for which the lack of an effective interfacial tension poses deep conceptual problems in the mathematical formulation of a linear stability analysis. Finally, we provide a short overview on the ongoing research on the effective, out of equilibrium interfacial tension between miscible fluids.
Gao, Kang; Gao, Wei; Wu, Di; Song, Chongmin
2018-02-01
This paper focuses on the dynamic stability behaviors of the functionally graded (FG) orthotropic circular cylindrical shell surrounded by the two-parameter (Winkler-Pasternak) elastic foundation subjected to a linearly increasing load with the consideration of damping effect. The material properties are assumed to vary gradually in the thickness direction based on an exponential distribution function of the volume fraction of constituent materials. Equations of motion are derived from Hamilton's principle and the nonlinear compatibility equation is considered by the means of modified Donnell shell theory including large deflection. Then the nonlinear dynamic buckling equation is solved by a hybrid analytical-numerical method (combined Galerkin method and fourth-order Runge-Kutta method). The nonlinear dynamic stability of the FG orthotropic cylindrical shell is assessed based on Budiansky-Roth criterion. Additionally, effects of different parameters such as various inhomogeneous parameters, loading speeds, damping ratios and aspect ratios and thickness ratios of the structure on dynamic buckling are discussed in details. Finally, the proposed method is validated with published literature.
Directory of Open Access Journals (Sweden)
Jeehyun Jung
2016-01-01
Full Text Available A dynamic model for a ball-end milling process that includes the consideration of cutting force nonlinearities and regenerative chatter effects is presented. The nonlinear cutting force is approximated using a Fourier series and then expanded into a Taylor series up to the third order. A series of nonlinear analyses was performed to investigate the nonlinear dynamic behavior of a ball-end milling system, and the differences between the nonlinear analysis approach and its linear counterpart were examined. A bifurcation analysis of points near the critical equilibrium points was performed using the method of multiple scales (MMS and the method of harmonic balance (MHB to analyse the local chatter behaviors of the system. The bifurcation analysis was conducted at two subcritical Hopf bifurcation points. It was also found that a ball-end milling system with nonlinear cutting forces near its critical equilibrium points is conditionally stable. The analysis and simulation results were compared with experimental data reported in the literature, and the physical significance of the results is discussed.
Elasto-hydrodynamic lubrication
Dowson, D; Hopkins, D W
1977-01-01
Elasto-Hydrodynamic Lubrication deals with the mechanism of elasto-hydrodynamic lubrication, that is, the lubrication regime in operation over the small areas where machine components are in nominal point or line contact. The lubrication of rigid contacts is discussed, along with the effects of high pressure on the lubricant and bounding solids. The governing equations for the solution of elasto-hydrodynamic problems are presented.Comprised of 13 chapters, this volume begins with an overview of elasto-hydrodynamic lubrication and representation of contacts by cylinders, followed by a discussio
Elementary classical hydrodynamics
Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C
1967-01-01
Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c
Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen
2018-01-01
In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.
International Nuclear Information System (INIS)
Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C
2006-01-01
With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods
The RAGE radiation-hydrodynamic code
Energy Technology Data Exchange (ETDEWEB)
Gittings, Michael; Clover, Michael; Betlach, Thomas; Byrne, Nelson; Ranta, Dale [Science Applications International Corp. MS A-1, 10260 Campus Point Drive, San Diego, CA 92121 (United States); Weaver, Robert; Coker, Robert; Dendy, Edward; Hueckstaedt, Robert; New, Kim; Oakes, W Rob [Los Alamos National Laboratory, MS T087, PO Box 1663, Los Alamos, NM 87545 (United States); Stefan, Ryan [TaylorMade-adidas Golf, 5545 Fermi Court, Carlsbad, CA 92008-7324 (United States)], E-mail: michael.r.clover@saic.com
2008-10-01
We describe RAGE, the 'radiation adaptive grid Eulerian' radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation-material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm.
The RAGE radiation-hydrodynamic code
International Nuclear Information System (INIS)
Gittings, Michael; Clover, Michael; Betlach, Thomas; Byrne, Nelson; Ranta, Dale; Weaver, Robert; Coker, Robert; Dendy, Edward; Hueckstaedt, Robert; New, Kim; Oakes, W Rob; Stefan, Ryan
2008-01-01
We describe RAGE, the 'radiation adaptive grid Eulerian' radiation-hydrodynamics code, including its data structures, its parallelization strategy and performance, its hydrodynamic algorithm(s), its (gray) radiation diffusion algorithm, and some of the considerable amount of verification and validation efforts. The hydrodynamics is a basic Godunov solver, to which we have made significant improvements to increase the advection algorithm's robustness and to converge stiffnesses in the equation of state. Similarly, the radiation transport is a basic gray diffusion, but our treatment of the radiation-material coupling, wherein we converge nonlinearities in a novel manner to allow larger timesteps and more robust behavior, can be applied to any multi-group transport algorithm
Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian
2018-01-01
In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.
Directory of Open Access Journals (Sweden)
Qianqian Yang
2010-01-01
fractional Fokker-Planck equations with a nonlinear source term (TSFFPENST, which involve the Caputo time fractional derivative (CTFD of order ∈ (0, 1 and the symmetric Riesz space fractional derivative (RSFD of order ∈ (1, 2]. Approximating the CTFD and RSFD using the L1-algorithm and shifted Grünwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.
Annual Report: Hydrodynamics and Radiative Hydrodynamics with Astrophysical Applications
Energy Technology Data Exchange (ETDEWEB)
R. Paul Drake
2005-12-01
We report the ongoing work of our group in hydrodynamics and radiative hydrodynamics with astrophysical applications. During the period of the existing grant, we have carried out two types of experiments at the Omega laser. One set of experiments has studied radiatively collapsing shocks, obtaining high-quality scaling data using a backlit pinhole and obtaining the first (ever, anywhere) Thomson-scattering data from a radiative shock. Other experiments have studied the deeply nonlinear development of the Rayleigh-Taylor (RT) instability from complex initial conditions, obtaining the first (ever, anywhere) dual-axis radiographic data using backlit pinholes and ungated detectors. All these experiments have applications to astrophysics, discussed in the corresponding papers either in print or in preparation. We also have obtained preliminary radiographs of experimental targets using our x-ray source. The targets for the experiments have been assembled at Michigan, where we also prepare many of the simple components. The above activities, in addition to a variety of data analysis and design projects, provide good experience for graduate and undergraduates students. In the process of doing this research we have built a research group that uses such work to train junior scientists.
Qin, Shunda; Ge, Hongxia; Cheng, Rongjun
2018-02-01
In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Hydrodynamic Coefficients Identification and Experimental Investigation for an Underwater Vehicle
Directory of Open Access Journals (Sweden)
Shaorong XIE
2014-02-01
Full Text Available Hydrodynamic coefficients are the foundation of unmanned underwater vehicles modeling and controller design. In order to reduce identification complexity and acquire necessary hydrodynamic coefficients for controllers design, the motion of the unmanned underwater vehicle was separated into vertical motion and horizontal motion models. Hydrodynamic coefficients were regarded as mapping parameters from input forces and moments to output velocities and acceleration of the unmanned underwater vehicle. The motion models of the unmanned underwater vehicle were nonlinear and Genetic Algorithm was adopted to identify those hydrodynamic coefficients. To verify the identification quality, velocities and acceleration of the unmanned underwater vehicle was measured using inertial sensor under the same conditions as Genetic Algorithm identification. Curves similarity between measured velocities and acceleration and those identified by Genetic Algorithm were used as optimizing standard. It is found that the curves similarity were high and identified hydrodynamic coefficients of the unmanned underwater vehicle satisfied the measured motion states well.
Tian, Jun-Fang; Yuan, Zhen-Zhou; Jia, Bin; Fan, Hong-Qiang
2013-03-01
We investigate the phase transitions and the Korteweg-de Vries (KdV) equation in the density difference lattice hydrodynamic (DDLM) model, which shows a close connection with the gas-kinetic-based model and the microscopic car following model. The KdV equation near the neutral stability line is derived and the corresponding soliton solution describing the density waves is obtained. Numerical simulations are conducted in two aspects. On the one hand, under periodic conditions perturbations are applied to demonstrate the nonlinear analysis result. On the other hand, the open boundary condition with random fluctuations is designed to explore the empirical congested traffic patterns. The phase transitions among the free traffic (FT), widening synchronized flow pattern (WSP), moving localized cluster (MLC), oscillatory congested traffic (OCT) and homogeneous congested traffic (HCT) occur by varying the amplitude of the fluctuations. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce so many congested traffic patterns.
Rajasekhar, Bathula; Bodavarapu, Navya; Sridevi, M.; Thamizhselvi, G.; RizhaNazar, K.; Padmanaban, R.; Swu, Toka
2018-03-01
The present study reports the synthesis and evaluation of nonlinear optical property and G-Quadruplex DNA Stabilization of five novel copper(II) mixed ligand complexes. They were synthesized from copper(II) salt, 2,5- and 2,3- pyridinedicarboxylic acid, diethylenetriamine and amide based ligand (AL). The crystal structure of these complexes were determined through X-ray diffraction and supported by ESI-MAS, NMR, UV-Vis and FT-IR spectroscopic methods. Their nonlinear optical property was studied using Gaussian09 computer program. For structural optimization and nonlinear optical property, density functional theory (DFT) based B3LYP method was used with LANL2DZ basis set for metal ion and 6-31G∗ for C,H,N,O and Cl atoms. The present work reveals that pre-polarized Complex-2 showed higher β value (29.59 × 10-30e.s.u) as compared to that of neutral complex-1 (β = 0.276 × 10-30e.s.u.) which may be due to greater advantage of polarizability. Complex-2 is expected to be a potential material for optoelectronic and photonic technologies. Docking studies using AutodockVina revealed that complex-2 has higher binding energy for both G-Quadruplex DNA (-8.7 kcal/mol) and duplex DNA (-10.1 kcal/mol). It was also observed that structure plays an important role in binding efficiency.
Doyon, Benjamin; Dubail, Jérôme; Konik, Robert; Yoshimura, Takato
2017-11-10
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
Doyon, Benjamin; Dubail, Jérôme; Konik, Robert; Yoshimura, Takato
2017-11-01
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
Integration of quantum hydrodynamical equation
Ulyanova, Vera G.; Sanin, Andrey L.
2007-04-01
Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.
Bhattacharjee, Amitava
2012-01-01
To celebrate Professor Robert Dewar's 65th birthday, a Symposium was held on 31 October 2009 in Atlanta, Georgia, just before the 51st Annual Meeting of the Division of Plasma Physics of the American Physical Society. The Symposium was attended by many of Bob's colleagues, friends, postdoctoral colleagues and students (present and former). Boyd Blackwell, Anthony Cooper, Chris Hegna, Stuart Hudson, John Krommes, Alexander Pletzer, Ellen Zweibel, and I gave talks that covered various aspects of Bob's wide-ranging scholarship, and his leadership in the Australian and the US fusion program. At the Symposium, Bob gave an insightful talk, published in this issue as a paper with D Leykam. This paper makes available for the first time unpublished results from Bob's M Sc Thesis on a general method for calculating the potential around a `dressed' test particle in an isotropic and collisionless plasma. The paper is interesting not only because it provides a glimpse of the type of elegant applied mathematics that we have come to associate with Bob, but also because he discusses some leitmotifs in his intellectual evolution since the time he was a graduate student at the University of Melbourne and Princeton University. Through his early encounter with quantum field theory, Bob appreciated the power of Lagrangian and Hamiltonian formalisms, which he used with great effectiveness in nonlinear dynamics and plasma physics. A question that animates much of his work is one that underlies the `dressed' particle problem: if one is given a Hamiltonian with an unperturbed (or `bare') part and an interaction part, how is one to obtain a canonical transformation to `the oscillation centre' thatwould reduce the interaction part to an irreducible residual part while incorporating the rest in a renormalized zeroth-order Hamiltonian? One summer in Princeton, I worked with Bob on a possible variational formulation for this problem, and failed. I was daunted enough by my failure that I turned
Dynamic structurization in solutions of hydrodynamically active polymers
International Nuclear Information System (INIS)
Pogrebnyak, V.G.; Tverdokhleb, S.V.; Naumchuk, N.V.
1993-01-01
The processes of ordering and self-regulation in nonlinear systems have attracted great attention because understanding the principles of self-regulation and its thermodynamics can become a clue to many physical phenomena. In this work, it is experimentally established that, under the condition of elongational flows, dynamic structurization and periodic processes may originate in the solutions of flexible, hydrodynamically-active polymers due to self-regulation in these systems. The hydrodynamic elongational field was created using the flow of a Newtonian liquid (water, acetone, dioxane) converging to a small opening. The hydrodynamically-active polymers were polyethylene oxide or hydrolyzed polyacrylamide
Effect of forward looking sites on a multi-phase lattice hydrodynamic model
Redhu, Poonam; Gupta, Arvind Kumar
2016-03-01
A new multi-phase lattice hydrodynamic traffic flow model is proposed by considering the effect of multi-forward looking sites on a unidirectional highway. We examined the qualitative properties of proposed model through linear as well as nonlinear stability analysis. It is shown that the multi-anticipation effect can significantly enlarge the stability region on the phase diagram and exhibit three-phase traffic flow. It is also observed that the multi-forward looking sites have prominent influence on traffic flow when driver senses the relative flux of leading vehicles. Theoretical findings are verified using numerical simulation which confirms that the traffic jam is suppressed efficiently by considering the information of leading vehicles in unidirectional multi-phase traffic flow.
Huang, D; Chernyshenko, S; Goulart, P; Lasagna, D; Tutty, O; Fuentes, F
2015-11-08
With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterizing the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares of polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterizing the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study, several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach.
Simon, J. S.; Valavani, L.
1991-01-01
The use of a closed-loop control to allow surge-free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described directly addresses the nonlinear nature of the compressor characteristic using a Liapunov-based control law design formulation. The proposed approach is fairly generic and should be of interest for gas turbine engines as well as other applications.
International Nuclear Information System (INIS)
Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.; Cothran, C.D.; Brown, M.R.; Schaffer, M.J.
2004-01-01
Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by the counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good agreement with results from the SSX-FRC experiment. Simulations show formation of an FRC in about 30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects
Campo, J L; Gil, M G
1993-01-12
Assortative or random mating following selection in either direction on a non-linear index (experiment 1) or stabilizing selection for pupal length (experiment 2) were carried out for five generations in two lines of Tribolium castaneum (A and R, respectively), with three replicates each. The selected proportion was 25% in all lines. In experiment 1, the selection criterion was designed to increase the aggregate value of adult weight and the first- and second-order powers of pupal length. The A and R lines gave significant responses for the aggregate value (184 ± 6 and 161 ± 14, respectively), pupal length (0.74 ± 0.02 and 0.64 ± 0.05, respectively), and adult weight (0.79 ± 0.03 and 0.78 ± 0.12, respectively). Although the A line was not significantly better than the R line, there was a consistent advantage for assortative mating over random mating, the mean response for aggregate value and pupal length being approximately 1.15 times greater for the A line. In experiment 2 the selection criterion was the square of the deviation from the mean pupal length (stabilizing selection); both lines did not show any change for pupal length. The phenotypic variance showed a significant decrease in the A and R lines, due to a decrease in between-family variance. The assortatively and randomly mated lines were similar for these changes in phenotypic variation. RESUMEN: Aparemiento clasificado y selección direccional o estabilizante para una función no lineal en Tribolium. Dos líneas de Tribolium castaneum fueron seleccionadas direccionalmente para un índice no lineal (experimento 1) o estabilizantemente para longitud de pupa (experimento 2), apareando los animales seleccionados clasificadamente (A) o aleatoriamente (R). Había tres repeticiones por experimento y línea, siendo la proporción de selección el 25%. En el experimento 1, el objetivo de selección incluía el peso adulto así como la longitud de pupa y su cuadrado. Ambas líneas dieron respuesta
Stability Analysis of a Turbocharger Rotor System Supported on Floating Ring Bearings
International Nuclear Information System (INIS)
Zhang, H; Shi, Z Q; Zhen, D; Gu, F S; Ball, A D
2012-01-01
The stability of a turbocharger rotor is governed by the coupling of rotor dynamics and fluid dynamics because the high speed rotor system is supported on a pair of hydrodynamic floating ring bearings which comprise of inner and outer fluid films in series. In order to investigate the stability, this paper has developed a finite element model of the rotor system with consideration of such exciting forces as rotor imbalance, hydrodynamic fluid forces, lubricant feed pressure and dead weight. The dimensionless analytical expression of nonlinear oil film forces in floating ring bearings have been derived on the basis of short bearing theory. Based on numerical simulation, the effects of rotor imbalance, lubricant viscosity, lubricant feed pressure and bearing clearances on the stability of turbocharger rotor system have been studied. The disciplines of the stability of two films and dynamic performances of rotor system have been provided.
Timonin, A. M.
2013-09-01
A square-law version of the geometrically nonlinear theory of bending of laminated composites with account of transverse normal and transverse shear strains is developed. The finite-layer method is used to analyze the effect of geometric nonlinearity on the stresses and deflections of an adhesively bonded joint and to reveal and estimate the stability of various equilibrium forms of a laminated plate with delaminations under compression.
Stabilizing local boundary conditions for two-dimensional shallow water equations
Dia, Ben Mansour
2018-03-27
In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.
Directory of Open Access Journals (Sweden)
Muhammad H. Al-Malack
2016-07-01
Full Text Available Fuel oil flyash (FFA produced in power and water desalination plants firing crude oils in the Kingdom of Saudi Arabia is being disposed in landfills, which increases the burden on the environment, therefore, FFA utilization must be encouraged. In the current research, the effect of adding FFA on the engineering properties of two indigenous soils, namely sand and marl, was investigated. FFA was added at concentrations of 5%, 10% and 15% to both soils with and without the addition of Portland cement. Mixtures of the stabilized soils were thoroughly evaluated using compaction, California Bearing Ratio (CBR, unconfined compressive strength (USC and durability tests. Results of these tests indicated that stabilized sand mixtures could not attain the ACI strength requirements. However, marl was found to satisfy the ACI strength requirement when only 5% of FFA was added together with 5% of cement. When the FFA was increased to 10% and 15%, the mixture’s strength was found to decrease to values below the ACI requirements. Results of the Toxicity Characteristics Leaching Procedure (TCLP, which was performed on samples that passed the ACI requirements, indicated that FFA must be cautiously used in soil stabilization.
Real-time visualization of intracellular hydrodynamics in single living cells
Potma, Eric O.; Boeij, Wim P. de; Haastert, Peter J.M. van; Wiersma, Douwe A.
2001-01-01
Intracellular water concentrations in single living cells were visualized by nonlinear coherent anti-Stokes Raman scattering (CARS) microscopy. In combination with isotopic exchange measurements, CARS microscopy allowed the real-time observation of transient intracellular hydrodynamics at a high
Fluctuating hydrodynamics for ionic liquids
Energy Technology Data Exchange (ETDEWEB)
Lazaridis, Konstantinos [Department of Mathematics and Statistics, Washington State University, Pullman, 99163 (United States); Wickham, Logan [Department of Computer Science, Washington State University, Richland, 99354 (United States); Voulgarakis, Nikolaos, E-mail: n.voulgarakis@wsu.edu [Department of Mathematics and Statistics, Washington State University, Pullman, 99163 (United States)
2017-04-25
We present a mean-field fluctuating hydrodynamics (FHD) method for studying the structural and transport properties of ionic liquids in bulk and near electrified surfaces. The free energy of the system consists of two competing terms: (1) a Landau–Lifshitz functional that models the spontaneous separation of the ionic groups, and (2) the standard mean-field electrostatic interaction between the ions in the liquid. The numerical approach used to solve the resulting FHD-Poisson equations is very efficient and models thermal fluctuations with remarkable accuracy. Such density fluctuations are sufficiently strong to excite the experimentally observed spontaneous formation of liquid nano-domains. Statistical analysis of our simulations provides quantitative information about the properties of ionic liquids, such as the mixing quality, stability, and the size of the nano-domains. Our model, thus, can be adequately parameterized by directly comparing our prediction with experimental measurements and all-atom simulations. Conclusively, this work can serve as a practical mathematical tool for testing various theories and designing more efficient mixtures of ionic liquids. - Highlights: • A new fluctuating hydrodynamics method for ionic liquids. • Description of ionic liquid morphology in bulk and near electrified surfaces. • Direct comparison with experimental measurements.
International Nuclear Information System (INIS)
Frank, T.D.
2011-01-01
Highlights: → RNA cross-replication is a marginally stable but not asymptotically stable process. → RNA enzymes exhibits a generalized logistic growth pattern with exponent equal to 2. → Degradation results in non-symmetric saturation levels of cross-replicating RNAs. -- Abstract: It is nowadays believed that the evolution of life involved as an intermediate step an RNA world. In such an RNA world RNA molecules replicate themselves in catalytic reactions. Recent experiments on cross-replicating RNA support the RNA world hypothesis. We derive a nonlinear mass-action kinetics model to explain logistic growth patterns and non-symmetric saturation levels observed in those experiments. We also demonstrate that fixed points of the RNA growth process are only marginally stable rather than asymptotically stable.
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Directory of Open Access Journals (Sweden)
Nikolai N. Bogoliubov (Jr.
2007-01-01
Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Transversal expansion study in the Landau hydrodynamic
International Nuclear Information System (INIS)
Pottag, F.W.
1984-01-01
The system of equations in the frame of Landau's hydrodynamical model for multiparticle production at high energies is studied. Taking as a first approximation the one-dimensional exact due to Khalatnikov, and a special set of curvilinear coordinates, the radial part is separated from the longitudinal one in the equations of motion, and a system of partial differential equations (non-linear, hyperbolic) is obtained for the radial part. These equations are solved numerically by the method of caracteristics. The hydrodynamical variables are obtained over all the three-dimensional-flow region as well as its variation with the mass of the initially expanding system. Both, the transverse rapidity distribution of the fluid and the inclusive particle distribution at 90 0 in the center of mass system, are calculated. The last one is compared with recent experimental data. (author) [pt
Radiative and hydrodynamic growth of the fireball
International Nuclear Information System (INIS)
Stanic, B.V.; Skoric, M.M.; Aleksic, Z.
1984-01-01
The radiative and the hydrodynamic phases in development of the fireball, which form following an intense source of x-rays released in the atmosphere, are discussed. In the forst section, physical principles and simplified model of the fireball growth in the radiative phase are presented. The system of nonlinear differential equations which describes the time evolution of the fireball parameters (radius and temperature) in the radiation diffusion phase is numerically solved. A relation to some earlier work is outlined. In the second section, the later phase of the growth of the fireball is described by the equations of classical hydrodynamics. relevant parameters of the fireball (pressure and density at the surface of the fireball, radius and velocity of shock front) are estimated for two values of adiabatic constant. (author)
Hydrodynamic Vortex on Surfaces
Ragazzo, Clodoaldo Grotta; de Barros Viglioni, Humberto Henrique
2017-10-01
The equations of motion for a system of point vortices on an oriented Riemannian surface of finite topological type are presented. The equations are obtained from a Green's function on the surface. The uniqueness of the Green's function is established under hydrodynamic conditions at the surface's boundaries and ends. The hydrodynamic force on a point vortex is computed using a new weak formulation of Euler's equation adapted to the point vortex context. An analogy between the hydrodynamic force on a massive point vortex and the electromagnetic force on a massive electric charge is presented as well as the equations of motion for massive vortices. Any noncompact Riemann surface admits a unique Riemannian metric such that a single vortex in the surface does not move ("Steady Vortex Metric"). Some examples of surfaces with steady vortex metric isometrically embedded in R^3 are presented.
Equilibration in one-dimensional quantum hydrodynamic systems
Sotiriadis, Spyros
2017-10-01
We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady state is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems. Dedicated to John Cardy on the occasion of his 70th birthday.
Nonlinear differential equations
Struble, Raimond A
2017-01-01
Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Directory of Open Access Journals (Sweden)
P. P. Hallan
2008-01-01
Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.
Song, Yongli; Makarov, Valeri A; Velarde, Manuel G
2009-08-01
A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.
Hydrodynamic Cavitation Reactors contd…
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Hydrodynamic Cavitation Reactors contd… Reservoir: 10 L capacity. Centrifugal Pump :1.5kW). Orifice plate (different configurations in terms of number and diameter of the holes). Bypass line (for controlling the inlet pressure and the flow rate into the cavitation ...
Dissipative relativistic hydrodynamics
International Nuclear Information System (INIS)
Imshennik, V.S.; Morozov, Yu.I.
1989-01-01
Using the comoving reference frame in the general non-inertial case, the relativistic hydrodynamics equations are derived with an account for dissipative effects in the matter. From the entropy production equation, the exact from for the dissipative tensor components is obtained. As a result, the closed system of equations of dissipative relativistic hydrodynamics is obtained in the comoving reference frame as a relativistic generalization of the known Navier-Stokes equations for Lagrange coordinates. Equations of relativistic hydrodynamics with account for dissipative effects in the matter are derived using the assocoated reference system in general non-inertial case. True form of the dissipative tensor components is obtained from entropy production equation. Closed system of equations for dissipative relativistic hydrodynamics is obtained as a result in the assocoated reference system (ARS) - relativistic generalization of well-known Navier-Stokes equations for Lagrange coordinates. Equation system, obtained in this paper for ARS, may be effectively used in numerical models of explosive processes with 10 51 erg energy releases which are characteristic for flashes of supernovae, if white dwarf type compact target suggested as presupernova
Nonlinear H∞ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation
Directory of Open Access Journals (Sweden)
Zool H. Ismail
2013-01-01
Full Text Available A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV with region tracking function. Within this control scheme, nonlinear H∞ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.
International Nuclear Information System (INIS)
Dorning, J.J.
1993-05-01
All the objectives originally scheduled for the first year of this grant have been achieved. Furthermore, the project is ahead of schedule, in that a substantial amount of work has been completed on two significant objectives originally planned for the second year. This interim report is divided into five parts, summarizing the mathematical development, analysis and results of the project goals -- goals originally planned for the first year and completed, and those on which substantial progress has been made ahead of schedule. Effects of unheated riser sections and the downcomer recirculation loop on the stability characteristics of advanced boiling water reactor designs that incorporate risers or unheated channel extensions are summarized in Part A. Such extensions are incorporated above the heated reactor core channels to enhance buoyancy-driven natural thermal convection both during normal at-power operation and during emergency shutdown. The effects of both, the inclusion of unheated riser sections in the designs (one of the goals substantially completed ahead of schedule), and the inclusion of the recirculation loop in the models (first year goal) were generally found to be destabilizing. In general, as riser lengths were increased equilibria that previously were stable became unstable, and the systems with the taller risers evolved to density-wave limit cycle oscillations. As a building block of the second year goal -- to extend the one dimensional dynamical analysis of reactor thermal-hydraulics/neutron-kinetics to two and three dimensions -- we have carried out, ahead of schedule, the nonlinear dynamical analysis of two-phase flow in multiple parallel heated channels. Some basic aspects of bifurcation phenomena in two-phase flow and the related nonlinear dynamics of single and multiple parallel, uniformly and nonuniformly heated channels are studied
Microflow Cytometers with Integrated Hydrodynamic Focusing
Directory of Open Access Journals (Sweden)
Martin Schmidt
2013-04-01
Full Text Available This study demonstrates the suitability of microfluidic structures for high throughput blood cell analysis. The microfluidic chips exploit fully integrated hydrodynamic focusing based on two different concepts: Two-stage cascade focusing and spin focusing (vortex principle. The sample—A suspension of micro particles or blood cells—is injected into a sheath fluid streaming at a substantially higher flow rate, which assures positioning of the particles in the center of the flow channel. Particle velocities of a few m/s are achieved as required for high throughput blood cell analysis. The stability of hydrodynamic particle positioning was evaluated by measuring the pulse heights distributions of fluorescence signals from calibration beads. Quantitative assessment based on coefficient of variation for the fluorescence intensity distributions resulted in a value of about 3% determined for the micro-device exploiting cascade hydrodynamic focusing. For the spin focusing approach similar values were achieved for sample flow rates being 1.5 times lower. Our results indicate that the performances of both variants of hydrodynamic focusing suit for blood cell differentiation and counting. The potential of the micro flow cytometer is demonstrated by detecting immunologically labeled CD3 positive and CD4 positive T-lymphocytes in blood.
International Nuclear Information System (INIS)
Zelenyj, L.M.; Kuznetsova, M.M.
1989-01-01
Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed
Zhu, Wenlong; Ma, Shoufeng; Tian, Junfang; Li, Geng
2016-11-01
Travelers' route adjustment behaviors in a congested road traffic network are acknowledged as a dynamic game process between them. Existing Proportional-Switch Adjustment Process (PSAP) models have been extensively investigated to characterize travelers' route choice behaviors; PSAP has concise structure and intuitive behavior rule. Unfortunately most of which have some limitations, i.e., the flow over adjustment problem for the discrete PSAP model, the absolute cost differences route adjustment problem, etc. This paper proposes a relative-Proportion-based Route Adjustment Process (rePRAP) maintains the advantages of PSAP and overcomes these limitations. The rePRAP describes the situation that travelers on higher cost route switch to those with lower cost at the rate that is unilaterally depended on the relative cost differences between higher cost route and its alternatives. It is verified to be consistent with the principle of the rational behavior adjustment process. The equivalence among user equilibrium, stationary path flow pattern and stationary link flow pattern is established, which can be applied to judge whether a given network traffic flow has reached UE or not by detecting the stationary or non-stationary state of link flow pattern. The stability theorem is proved by the Lyapunov function approach. A simple example is tested to demonstrate the effectiveness of the rePRAP model.
Vibration of a rotating shaft on hydrodynamic bearings: multi-scales surface effects
International Nuclear Information System (INIS)
Rebufa, Jocelyn
2016-01-01
The hydrodynamic bearing provides good damping properties in rotating machineries. However, the performances of rotor-bearings systems are highly impacted by nonlinear effects that are difficult to analyze. The rotor dynamics prediction requires advanced models for the flow in the bearings. The surface of the bearings seems to have a strong impact on the lubricant flow, acting on the static and dynamic properties of the rotating parts. This study aims to enhance the simulation of the bearings' surface state effect on the motion of the rotating shaft. The flexible shaft interacts with textured hydrodynamic bearings. Multi-scales homogenization is used in a multi-physics algorithm in order to describe the fluid-structure interaction. Different models are used to account for the cavitation phenomenon in the bearings. Nonlinear harmonic methods allow efficient parametric studies of periodic solutions as well as their stability. Moreover, a test rig has been designed to compare predictions to real measurements. Several textured shaft samples modified with femto-seconds LASER surface texturing are tested. In most cases the experimental study showed similar results than the simulation. Enhancements of the vibration behaviors of the rotor-bearing system have been revealed for certain texturing patterns. The self-excited vibration, also known as 'oil whirl' phenomenon, is stabilized on a wide rotating frequency range. However, the simulation tool does not predict well the enhancements that are observed. Vortices in surface texturing patterns have been revealed numerically with Navier-Stokes equation resolution. These results are opposed to the classical lubrication hypothesis. It is also a possible explanation of the enhancements that are experimentally measured with textured bearings. (author) [fr
Directory of Open Access Journals (Sweden)
Abdelraheem M. Aly
2015-02-01
Full Text Available A stabilized incompressible smoothed particle hydrodynamics (ISPH method with the addition of a density invariant relaxation condition in the pressure calculations is applied to simulations of highly nonlinear liquid sloshing problems. By applying the Neumann boundary condition when solving pressure, the performance of the present ISPH method is enhanced significantly. Two large-amplitude free sloshing problems under a resonance sway excitation were carried out in a square and a rectangular tank with filling-depths ratios of 20% and 50% of tank height, respectively, and compared with the available published experimental results. To extend the validation of the method, numerical simulations for sloshing problems with the varying density of a floating body as well as a middle baffle, which also generates strongly nonlinear free surface flow, were conducted. The results showed that the present ISPH method produces smooth pressure distribution and significantly reduces spurious oscillation. The proposed ISPH method was shown to be robust and accurate in long time simulation of highly nonlinear sloshing problems.
Hydrodynamics of insect spermatozoa
Pak, On Shun; Lauga, Eric
2010-11-01
Microorganism motility plays important roles in many biological processes including reproduction. Many microorganisms propel themselves by propagating traveling waves along their flagella. Depending on the species, propagation of planar waves (e.g. Ceratium) and helical waves (e.g. Trichomonas) were observed in eukaryotic flagellar motion, and hydrodynamic models for both were proposed in the past. However, the motility of insect spermatozoa remains largely unexplored. An interesting morphological feature of such cells, first observed in Tenebrio molitor and Bacillus rossius, is the double helical deformation pattern along the flagella, which is characterized by the presence of two superimposed helical flagellar waves (one with a large amplitude and low frequency, and the other with a small amplitude and high frequency). Here we present the first hydrodynamic investigation of the locomotion of insect spermatozoa. The swimming kinematics, trajectories and hydrodynamic efficiency of the swimmer are computed based on the prescribed double helical deformation pattern. We then compare our theoretical predictions with experimental measurements, and explore the dependence of the swimming performance on the geometric and dynamical parameters.
Nonlinear Analysis and Variational Problems
Pardalos, Panos M
2010-01-01
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization. "Nonlinear Analysis and Variational Problems" is organized into two parts. Part I, Nonlinear Analysis, centers on stability issues for functional equations, fixed point
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
How to fake hydrodynamic signals
Energy Technology Data Exchange (ETDEWEB)
Romatschke, Paul [Department of Physics, 390 UCB, University of Colorado at Boulder, Boulder, CO (United States); Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309 (United States)
2016-12-15
Flow signatures in experimental data from relativistic ion collisions, are usually interpreted as a fingerprint of the presence of a hydrodynamic phase during the evolution of these systems. I review some theoretical ideas to ‘fake’ this hydrodynamic behavior in p+A and A+A collisions. I find that transverse flow and femtoscopic measurements can easily be forged through non-hydrodynamic evolution, while large elliptic flow requires some non-vanishing interactions in the hot phase.
Foundations of radiation hydrodynamics
Mihalas, Dimitri
1999-01-01
Radiation hydrodynamics is a broad subject that cuts across many disciplines in physics and astronomy: fluid dynamics, thermodynamics, statistical mechanics, kinetic theory, and radiative transfer, among others. The theory developed in this book by two specialists in the field can be applied to the study of such diverse astrophysical phenomena as stellar winds, supernova explosions, and the initial phases of cosmic expansion, as well as the physics of laser fusion and reentry vehicles. As such, it provides students with the basic tools for research on radiating flows.Largely self-contained,
Hydrodynamics of superfluid crystals
International Nuclear Information System (INIS)
Vardanyan, G.A.; Papoyan, K.V.; Sedrakyan, D.M.
1984-01-01
It is shown that three-velocity hydrodynamics equations describing the properties of a two-condensate crystal determine the low-frequency spectrum with allowance for superfluid drag. The drag on one superfluid component of density rho/sup( s/) 12 from another component of density rho/sup( s/) 22 , gives rise to two branches of vibrations of frequencies ω 1 and ω 2 , unlike the case of a one-condensate crystal. The absorption coefficient for transverse sound in a one-condensate crystal is expressed in terms of the quantum-mechanical characteristic quantity that describes the tunneling of atoms
Tiofack, C. G. L.; Ndzana, F., II; Mohamadou, A.; Kofane, T. C.
2018-03-01
We investigate the existence and stability of solitons in parity-time (PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT -breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.
Anisotropic nonequilibrium hydrodynamic attractor
Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.
2018-02-01
We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.
Nanoscale hydrodynamics near solids
Camargo, Diego; de la Torre, J. A.; Duque-Zumajo, D.; Español, Pep; Delgado-Buscalioni, Rafael; Chejne, Farid
2018-02-01
Density Functional Theory (DFT) is a successful and well-established theory for the study of the structure of simple and complex fluids at equilibrium. The theory has been generalized to dynamical situations when the underlying dynamics is diffusive as in, for example, colloidal systems. However, there is no such a clear foundation for Dynamic DFT (DDFT) for the case of simple fluids in contact with solid walls. In this work, we derive DDFT for simple fluids by including not only the mass density field but also the momentum density field of the fluid. The standard projection operator method based on the Kawasaki-Gunton operator is used for deriving the equations for the average value of these fields. The solid is described as featureless under the assumption that all the internal degrees of freedom of the solid relax much faster than those of the fluid (solid elasticity is irrelevant). The fluid moves according to a set of non-local hydrodynamic equations that include explicitly the forces due to the solid. These forces are of two types, reversible forces emerging from the free energy density functional, and accounting for impenetrability of the solid, and irreversible forces that involve the velocity of both the fluid and the solid. These forces are localized in the vicinity of the solid surface. The resulting hydrodynamic equations should allow one to study dynamical regimes of simple fluids in contact with solid objects in isothermal situations.
Load responsive hydrodynamic bearing
Kalsi, Manmohan S.; Somogyi, Dezso; Dietle, Lannie L.
2002-01-01
A load responsive hydrodynamic bearing is provided in the form of a thrust bearing or journal bearing for supporting, guiding and lubricating a relatively rotatable member to minimize wear thereof responsive to relative rotation under severe load. In the space between spaced relatively rotatable members and in the presence of a liquid or grease lubricant, one or more continuous ring shaped integral generally circular bearing bodies each define at least one dynamic surface and a plurality of support regions. Each of the support regions defines a static surface which is oriented in generally opposed relation with the dynamic surface for contact with one of the relatively rotatable members. A plurality of flexing regions are defined by the generally circular body of the bearing and are integral with and located between adjacent support regions. Each of the flexing regions has a first beam-like element being connected by an integral flexible hinge with one of the support regions and a second beam-like element having an integral flexible hinge connection with an adjacent support region. A least one local weakening geometry of the flexing region is located intermediate the first and second beam-like elements. In response to application of load from one of the relatively rotatable elements to the bearing, the beam-like elements and the local weakening geometry become flexed, causing the dynamic surface to deform and establish a hydrodynamic geometry for wedging lubricant into the dynamic interface.
Betchov, R
2012-01-01
Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equation
Fluctuating hydrodynamics for ionic liquids
Lazaridis, Konstantinos; Wickham, Logan; Voulgarakis, Nikolaos
2017-04-01
We present a mean-field fluctuating hydrodynamics (FHD) method for studying the structural and transport properties of ionic liquids in bulk and near electrified surfaces. The free energy of the system consists of two competing terms: (1) a Landau-Lifshitz functional that models the spontaneous separation of the ionic groups, and (2) the standard mean-field electrostatic interaction between the ions in the liquid. The numerical approach used to solve the resulting FHD-Poisson equations is very efficient and models thermal fluctuations with remarkable accuracy. Such density fluctuations are sufficiently strong to excite the experimentally observed spontaneous formation of liquid nano-domains. Statistical analysis of our simulations provides quantitative information about the properties of ionic liquids, such as the mixing quality, stability, and the size of the nano-domains. Our model, thus, can be adequately parameterized by directly comparing our prediction with experimental measurements and all-atom simulations. Conclusively, this work can serve as a practical mathematical tool for testing various theories and designing more efficient mixtures of ionic liquids.
Breatherlike excitations in discrete lattices with noise and nonlinear damping
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus
1997-01-01
We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...
Can non-propagating hydrodynamic solitons be forced to move?
Gordillo, L.; Sauma, T.; Zárate, Y.; Espinoza, I.; Clerc, M. G.; Mujica, N.
2011-03-01
Development of technologies based on localized states depends on our ability to manipulate and control these nonlinear structures. In order to achieve this, the interactions between localized states and control tools should be well modelled and understood. We present a theoretical and experimental study for handling non-propagating hydrodynamic solitons in a vertically driven rectangular water basin, based on the inclination of the system. Experiments show that tilting the basin induces non-propagating solitons to drift towards an equilibrium position through a relaxation process. Our theoretical approach is derived from the parametrically driven damped nonlinear Schrödinger equationwhich models the system. The basin tilting effect is modelled by promoting the parameters that characterize the system, e.g. dissipation, forcing and frequency detuning, as space dependent functions. A motion law for these hydrodynamic solitons can be deduced from these assumptions. The model equation, which includes a constant speed and a linear relaxation term, nicely reproduces the motion observed experimentally.
Eu, Byung Chan
2016-01-01
This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respe...
Hydrodynamic instabilities in an ablation front
Energy Technology Data Exchange (ETDEWEB)
Piriz, A R; Portugues, R F [E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)
2004-06-01
The hydrodynamic stability of an ablation front is studied for situations in which the wavelength of the perturbations is larger than the distance to the critical surface where the driving radiation is absorbed. An analytical model is presented, and it shows that under conditions in which the thermal flux is limited within the supercritical region of the ablative corona, the front may behave like a flame or like an ablation front, depending on the perturbation wavelength. For relatively long wavelengths the critical and ablation surfaces practically lump together into a unique surface and the front behaves like a flame, whereas for the shortest wavelengths the ablation front substructure is resolved.
Anomalous hydrodynamics in two dimensions
Indian Academy of Sciences (India)
Keywords. Anomalous hydrodynamics; gauge anomaly; gravitational anomaly. PACS No. 47.10.ab. The chiral anomaly has played a ubiquitous role in modern physics. It has found appli- cations in several diverse fields like quantum wires, quantum Hall effect, chiral magnetic effect and anomalous hydrodynamics, to name ...
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2010-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Newtonian hydrodynamic equations with relativistic pressure and velocity
Hwang, Jai-chan; Noh, Hyerim; Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried
2016-07-01
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.
Hydrodynamic processes in sharp meander bends and their morphological implications
Blanckaert, K.
2011-01-01
The migration rate of sharp meander bends exhibits large variance and indicates that some sharply curved bends tend to stabilize. These observations remain unexplained. This paper examines three hydrodynamic processes in sharp bends with fixed banks and discusses their morphological implications:
Phase transition of a new lattice hydrodynamic model with consideration of on-ramp and off-ramp
Zhang, Geng; Sun, Di-hua; Zhao, Min
2018-01-01
A new traffic lattice hydrodynamic model with consideration of on-ramp and off-ramp is proposed in this paper. The influence of on-ramp and off-ramp on the stability of the main road is uncovered by theoretical analysis and computer simulation. Through linear stability theory, the neutral stability condition of the new model is obtained and the results show that the unstable region in the phase diagram is enlarged by considering the on-ramp effect but shrunk with consideration of the off-ramp effect. The mKdV equation near the critical point is derived via nonlinear reductive perturbation method and the occurrence of traffic jamming transition can be described by the kink-antikink soliton solution of the mKdV equation. From the simulation results of space-time evolution of traffic density waves, it is shown that the on-ramp can worsen the traffic stability of the main road but off-ramp is positive in stabilizing the traffic flow of the main road.
Hydrodynamics of Peristaltic Propulsion
Athanassiadis, Athanasios; Hart, Douglas
2014-11-01
A curious class of animals called salps live in marine environments and self-propel by ejecting vortex rings much like jellyfish and squid. However, unlike other jetting creatures that siphon and eject water from one side of their body, salps produce vortex rings by pumping water through siphons on opposite ends of their hollow cylindrical bodies. In the simplest cases, it seems like some species of salp can successfully move by contracting just two siphons connected by an elastic body. When thought of as a chain of timed contractions, salp propulsion is reminiscent of peristaltic pumping applied to marine locomotion. Inspired by salps, we investigate the hydrodynamics of peristaltic propulsion, focusing on the scaling relationships that determine flow rate, thrust production, and energy usage in a model system. We discuss possible actuation methods for a model peristaltic vehicle, considering both the material and geometrical requirements for such a system.
International Nuclear Information System (INIS)
Koehler, H.S.
1983-01-01
The Time-Dependent Hartree-Fock theory provides a microscopic approach to the scattering of heavy ions. Fundamental in this theory is a mean-(one-body) field. The calculation of this field from a two-body effective interaction makes the theory microscopic. Many-body effects are included by the Brueckner definition of this interaction; the reaction-matrix. In excited media it is in general complex allowing for decays. The imaginary part relates directly to the collision-term in a transport equation. We treat this term by the time-relaxation-method. This implies an extension of the TDHF-equation to include two-body collisions. Hydrodynamic equations are derived from this new equation. The solution of the two equations agree quantitatively for short-relaxation-times. Relaxation-times are calculated as a function of temperature. (orig.)
Hydrodynamic effects on coalescence.
Energy Technology Data Exchange (ETDEWEB)
Dimiduk, Thomas G.; Bourdon, Christopher Jay; Grillet, Anne Mary; Baer, Thomas A.; de Boer, Maarten Pieter; Loewenberg, Michael (Yale University, New Haven, CT); Gorby, Allen D.; Brooks, Carlton, F.
2006-10-01
The goal of this project was to design, build and test novel diagnostics to probe the effect of hydrodynamic forces on coalescence dynamics. Our investigation focused on how a drop coalesces onto a flat surface which is analogous to two drops coalescing, but more amenable to precise experimental measurements. We designed and built a flow cell to create an axisymmetric compression flow which brings a drop onto a flat surface. A computer-controlled system manipulates the flow to steer the drop and maintain a symmetric flow. Particle image velocimetry was performed to confirm that the control system was delivering a well conditioned flow. To examine the dynamics of the coalescence, we implemented an interferometry capability to measure the drainage of the thin film between the drop and the surface during the coalescence process. A semi-automated analysis routine was developed which converts the dynamic interferogram series into drop shape evolution data.
Hydrodynamics of sediment threshold
Ali, Sk Zeeshan; Dey, Subhasish
2016-07-01
A novel hydrodynamic model for the threshold of cohesionless sediment particle motion under a steady unidirectional streamflow is presented. The hydrodynamic forces (drag and lift) acting on a solitary sediment particle resting over a closely packed bed formed by the identical sediment particles are the primary motivating forces. The drag force comprises of the form drag and form induced drag. The lift force includes the Saffman lift, Magnus lift, centrifugal lift, and turbulent lift. The points of action of the force system are appropriately obtained, for the first time, from the basics of micro-mechanics. The sediment threshold is envisioned as the rolling mode, which is the plausible mode to initiate a particle motion on the bed. The moment balance of the force system on the solitary particle about the pivoting point of rolling yields the governing equation. The conditions of sediment threshold under the hydraulically smooth, transitional, and rough flow regimes are examined. The effects of velocity fluctuations are addressed by applying the statistical theory of turbulence. This study shows that for a hindrance coefficient of 0.3, the threshold curve (threshold Shields parameter versus shear Reynolds number) has an excellent agreement with the experimental data of uniform sediments. However, most of the experimental data are bounded by the upper and lower limiting threshold curves, corresponding to the hindrance coefficients of 0.2 and 0.4, respectively. The threshold curve of this study is compared with those of previous researchers. The present model also agrees satisfactorily with the experimental data of nonuniform sediments.
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Arun, N K; Mohan, B M
2017-09-01
The mathematical models reported in the literature so far have been found using Center of Sums (CoS) defuzzification method only. It appears that no one has found models using Center of Area (CoA) or Center of Gravity (CoG) defuzzification method. Although there have been some works reported to deal with modeling of fuzzy controllers via Centroid method, all of them have in fact used CoS method only. In this paper, for the first time mathematical models of the simplest Mamdani type fuzzy Proportional Integral (PI)/Proportional Derivative (PD) controllers via CoG defuzzification are presented. L-type and Γ-type membership functions over different Universes of Discourse (UoDs) are considered for the input variables. L-type, Π-type and Γ-type membership functions are considered for the output variable. Three linear fuzzy control rules relating all four input fuzzy sets to three output fuzzy sets are chosen. Two triangular norms namely Algebraic Product (AP) and Minimum (Min), Maximum (Max) triangular co-norm, and two inference methods, Larsen Product (LP) and Mamdani Minimum (MM), are used. Properties of the models are studied. Stability analysis of closed-loop systems containing one of these controller models in the loop is done using the Small Gain theorem. Since digital controllers are implemented using digital processors, computational and memory requirements of these fuzzy controllers and conventional (nonfuzzy) controllers are compared. A rough estimate of the computational time taken by the digital computer while implementing any of these discrete-time fuzzy controllers is given. Two nonlinear plants are considered to show the superiority of the simplest fuzzy controller obtained using CoA or CoG defuzzification method over the simplest fuzzy controller obtained using CoS method and reported recently. Real-time implementation of one of the developed controller models is done on coupled tank experimental setup to show the feasibility of the developed model
Hydrodynamics of primordial black hole formation
Nadezhin, D. K.; Novikov, I. D.; Polnarev, A. G.
1979-01-01
The hydrodynamic picture of the formation of primordial black holes (PBH) at the early stages of expansion of the Universe is considered. It is assumed that close to singularity, expansion occurs in a quasi-isotropic way. Using an EVM, a spherically symmetrical nonlinear problem of the evolution of primary strong deviation from the Fridman solution was solved. What these deviations must be, so that the formation of PBH occurred was clarified. Attention was devoted to the role of pressure gradients. It is pointed out that at the moment of formation of PBH, only a small part of matter enters into it, primarily the component of perturbation. It is also pointed out that at this moment, the mass of PBH essentially is smaller than the mass considered within the cosmic horizon. The possibility of changing the mass of the PBH as a result of accretion is analyzed.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Hydrodynamic instability experiments on the Nova laser
International Nuclear Information System (INIS)
Remington, B.A.; Glendinning, S.G.; Kalantar, D.H.
1996-08-01
Hydrodynamic instabilities in compressible plasmas play a critical role in the fields of inertial confinement fusion (ICF), astrophysics, and high energy-density physics. We are, investigating hydrodynamic instabilities such as the Rayleigh-Taylor (RT) instability, at high compression at the Nova laser in a series of experiments, both in planar and in spherical geometry. In the indirect drive approach, a thermal x-ray drive is generated by focusing the Nova laser beams into a Au cylindrical radiation cavity (hohlraum). Issues in the instability evolution that we are examining are shock propagation and foil compression, RT growth of 2D versus 3D single-mode perturbations, drive pulse shape, perturbation location at the ablation front versus at an embedded interface, and multimode perturbation growth and nonlinear saturation. The effects of convergence on RT growth are being investigated both with hemispherical implosions of packages mounted on the hohlraum wall and with spherical implosions of capsules at the center of the hohlraum. Single-mode perturbations are pre-imposed at the ablation front of these capsules as a seed for the RT growth. In our direct drive experiments, we are investigating the effect of laser imprinting and subsequent RT growth on planar foils, both at λ Laser = 1/3 μm and 1/2 μm. An overview is given describing recent progress in each of these areas
Recent development of hydrodynamic modeling
Hirano, Tetsufumi
2014-09-01
In this talk, I give an overview of recent development in hydrodynamic modeling of high-energy nuclear collisions. First, I briefly discuss about current situation of hydrodynamic modeling by showing results from the integrated dynamical approach in which Monte-Carlo calculation of initial conditions, quark-gluon fluid dynamics and hadronic cascading are combined. In particular, I focus on rescattering effects of strange hadrons on final observables. Next I highlight three topics in recent development in hydrodynamic modeling. These include (1) medium response to jet propagation in di-jet asymmetric events, (2) causal hydrodynamic fluctuation and its application to Bjorken expansion and (3) chiral magnetic wave from anomalous hydrodynamic simulations. (1) Recent CMS data suggest the existence of QGP response to propagation of jets. To investigate this phenomenon, we solve hydrodynamic equations with source term which exhibits deposition of energy and momentum from jets. We find a large number of low momentum particles are emitted at large angle from jet axis. This gives a novel interpretation of the CMS data. (2) It has been claimed that a matter created even in p-p/p-A collisions may behave like a fluid. However, fluctuation effects would be important in such a small system. We formulate relativistic fluctuating hydrodynamics and apply it to Bjorken expansion. We found the final multiplicity fluctuates around the mean value even if initial condition is fixed. This effect is relatively important in peripheral A-A collisions and p-p/p-A collisions. (3) Anomalous transport of the quark-gluon fluid is predicted when extremely high magnetic field is applied. We investigate this possibility by solving anomalous hydrodynamic equations. We found the difference of the elliptic flow parameter between positive and negative particles appears due to the chiral magnetic wave. Finally, I provide some personal perspective of hydrodynamic modeling of high energy nuclear collisions
An analysis of smoothed particle hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Swegle, J.W.; Attaway, S.W.; Heinstein, M.W.; Mello, F.J. [Sandia National Labs., Albuquerque, NM (United States); Hicks, D.L. [Michigan Technological Univ., Houghton, MI (United States)
1994-03-01
SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine its applicability in the field of solid dynamics. An important result of the work is a rigorous von Neumann stability analysis which provides a simple criterion for the stability or instability of the method in terms of the stress state and the second derivative of the kernel function. Instability, which typically occurs only for solids in tension, results not from the numerical time integration algorithm, but because the SPH algorithm creates an effective stress with a negative modulus. The analysis provides insight into possible methods for removing the instability. Also, SPH has been coupled into the transient dynamics finite element code PRONTO, and a weighted residual derivation of the SPH equations has been obtained.
SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION
Energy Technology Data Exchange (ETDEWEB)
Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)
2016-12-20
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Ulrich, Elaine Schmid
Microfluidic networks and microporous materials have long been of interest in areas such as hydrology, petroleum engineering, chemical and electrochemical engineering, medicine and biochemical engineering. With the emergence of new processes in gas separation, cell sorting, ultrafiltration, and advanced materials synthesis, the importance of building a better qualitative and quantitative understanding of these key technologies has become apparent. However, microfluidic measurement and theory is still relatively underdeveloped, presenting a significant obstacle to the systematic design of microfluidic devices and materials. Theoretical challenges arise from the breakdown of classical viscous flow models as the flow dimensions approach the mean free path of individual molecules. Experimental challenges arise from the lack of flow profilometry techniques at sub-micron length scales. Here we present an extension of scanning probe microscopy techniques, which we have termed Hydrodynamic Force Microscopy (HFM). HFM exploits fluid drag to profile microflows and to map the permeability of microporous materials. In this technique, an atomic force microscope (AFM) cantilever is scanned close to a microporous sample surface. The hydrodynamic interactions arising from a pressure-driven flow through the sample are then detected by mapping the deflection of an AFM cantilever. For gas flows at atmospheric pressure, HFM has been shown to achieve a velocity sensitivity of 1 cm/s with a spatial resolution of ˜ 10 nm. This compares very favorably to established techniques such as hot-wire and laser Doppler anemometry, whose spatial resolutions typically exceed 1 mum and which may rely on the use of tracer particles or flow markers1. We demonstrate that HFM can successfully profile Poiseuille flows inside pores as small as 100 nm and can distinguish Poiseuille flow from uniform flow for short entry lengths. HFM detection of fluid jets escaping from porous samples can also reveal a
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.
2014-01-01
The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic
Engineering Hydrodynamic AUV Hulls
Allen, J.
2016-12-01
AUV stands for autonomous underwater vehicle. AUVs are used in oceanography and are similar to gliders. MBARIs AUVs as well as other AUVs map the ocean floor which is very important. They also measure physical characteristics of the water, such as temperature and salinity. My science fair project for 4th grade was a STEM activity in which I built and tested 3 different AUV bodies. I wanted to find out which design was the most hydrodynamic. I tested three different lengths of AUV hulls to see which AUV would glide the farthest. The first was 6 inches. The second was 12 inches and the third was 18 inches. I used clay for the nosecone and cut a ruler into two and made it the fin. Each AUV used the same nosecone and fin. I tested all three designs in a pool. I used biomimicry to create my hypothesis. When I was researching I found that long slim animals swim fastest. So, my hypothesis is the longer AUV will glide farthest. In the end I was right. The longer AUV did glide the farthest.
Advanced in Macrostatistical Hydrodynamics
International Nuclear Information System (INIS)
Graham, A.L.; Tetlow, N.; Abbott, J.R.; Mondy, L.S.; Brenner, H.
1993-01-01
An overview is presented of research that focuses on slow flows of suspensions in which colloidal and inertial effects are negligibly small (Macrostatistical Hydrodynamics). First, we describe nuclear magnetic resonance imaging experiments to quantitatively measure particle migration occurring in concentrated suspensions undergoing a flow with a nonuniform shear rate. These experiments address the issue of how the flow field affects the microstructure of suspensions. In order to understand the local viscosity in a suspension with such a flow-induced, spatially varying concentration, one must know how the viscosity of a homogeneous suspension depends on such variables as solids concentration and particle orientation. We suggest the technique of falling ball viscometry, using small balls, as a method to determine the effective viscosity of a suspension without affecting the original microstructure significantly. We also describe data from experiments in which the detailed fluctuations of a falling ball's velocity indicate the noncontinuum nature of the suspension and may lead to more insights into the effects of suspension microstructure on macroscopic properties. Finally, we briefly describe other experiments that can be performed in quiescent suspensions (in contrast to the use of conventional shear rotational viscometers) in order to learn more about the microstructure and boundary effects in concentrated suspensions
Lotic Water Hydrodynamic Model
Energy Technology Data Exchange (ETDEWEB)
Judi, David Ryan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tasseff, Byron Alexander [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-01-23
Water-related natural disasters, for example, floods and droughts, are among the most frequent and costly natural hazards, both socially and economically. Many of these floods are a result of excess rainfall collecting in streams and rivers, and subsequently overtopping banks and flowing overland into urban environments. Floods can cause physical damage to critical infrastructure and present health risks through the spread of waterborne diseases. Los Alamos National Laboratory (LANL) has developed Lotic, a state-of-the-art surface water hydrodynamic model, to simulate propagation of flood waves originating from a variety of events. Lotic is a two-dimensional (2D) flood model that has been used primarily for simulations in which overland water flows are characterized by movement in two dimensions, such as flood waves expected from rainfall-runoff events, storm surge, and tsunamis. In 2013, LANL developers enhanced Lotic through several development efforts. These developments included enhancements to the 2D simulation engine, including numerical formulation, computational efficiency developments, and visualization. Stakeholders can use simulation results to estimate infrastructure damage and cascading consequences within other sets of infrastructure, as well as to inform the development of flood mitigation strategies.
Hydrodynamics of electrons in graphene
Lucas, Andrew; Chung Fong, Kin
2018-02-01
Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the ‘phase diagram’ of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Hydrodynamic aspects of flotation separation
Directory of Open Access Journals (Sweden)
Peleka Efrosyni N.
2016-01-01
Full Text Available Flotation separation is mainly used for removing particulates from aqueous dispersions. It is widely used for ore beneficiation and recovering valuable materials. This paper reviews the hydrodynamics of flotation separations and comments on selected recent publications. Units are distinguished as cells of ideal and non-ideal flow. A brief introduction to hydrodynamics is included to explain an original study of the hybrid flotation-microfiltration cell, effective for heavy metal ion removal.
An introduction to astrophysical hydrodynamics
Shore, Steven N
1992-01-01
This book is an introduction to astrophysical hydrodynamics for both astronomy and physics students. It provides a comprehensive and unified view of the general problems associated with fluids in a cosmic context, with a discussion of fluid dynamics and plasma physics. It is the only book on hydrodynamics that addresses the astrophysical context. Researchers and students will find this work to be an exceptional reference. Contents include chapters on irrotational and rotational flows, turbulence, magnetohydrodynamics, and instabilities.
Pattern formation in flocking models: A hydrodynamic description
Solon, Alexandre P.; Caussin, Jean-Baptiste; Bartolo, Denis; Chaté, Hugues; Tailleur, Julien
2015-12-01
We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.
Pattern formation in flocking models: A hydrodynamic description.
Solon, Alexandre P; Caussin, Jean-Baptiste; Bartolo, Denis; Chaté, Hugues; Tailleur, Julien
2015-12-01
We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.
Ablation front hydrodynamic instability experiments on Nova
International Nuclear Information System (INIS)
Remington, B.A.; Marinak, M.M.; Weber, S.V.; Budil, K.S.; Landen, O.L.; Haan, S.W.; Wallace, R.J.
1995-01-01
The x-ray driven ablation front hydrodynamic instability experiments at Nova span 1988-present, and can be divided into three generations. The 1st generation experiments consisted of planar foils with perturbations of the form k = k x imposed on the drive side of the foil. A variety of drive pulse shapes, foil materials, and perturbation wavelengths and amplitudes were investigated, with growth factors of up to 80 being observed. The 2nd generation experiments investigated mode-mode interactions with imposed perturbations corresponding to the superposition of modes. They have done experiments with two-mode and eight-mode foils. In the linear regime, the modes grow independently with their own respective growth rates. In the nonlinear regime, in addition to the higher harmonics of the pre-existing modes, coupled terms k i ± k j occur. The 3rd generation experiments focus on 3D Rayleigh-Taylor growth. They have recently done experiments with an imposed 3D single-mode perturbation of the form k = (k x ,k y ), with k x = k y . In the linear regime, this perturbation grows exponentially with wave vector k = (k x 2 + k y 2 ) 1/2 . In the nonlinear regime, the perturbations evolve into broad bubbles surrounded on four corners by very dense, localized spikes with archways or saddle points in between. Simulations suggest that this 3D square mode grows larger than the corresponding 2D perturbation with the same magnitude wavevector and initial amplitude
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Delayed-feedback control in a Lattice hydrodynamic model
Redhu, Poonam; Gupta, Arvind Kumar
2015-10-01
The delayed-feedback control (DFC) method for lattice hydrodynamic traffic flow model is investigated on a unidirectional road. By using the Hurwitz criteria and the condition for transfer function in term of H∞ -norm, we designed the feedback gain and delay time to stabilize the traffic flow and suppress the traffic jam. The Bode-plot of transfer function have been plotted and discussed that the stability region enhances with delayed-feedback control. It is shown that the delayed-feedback control method stabilizes the traffic flow and suppresses the traffic jam efficiently. The simulation results are in good agreement with the theoretical analysis.
Instability thresholds for flexible rotors in hydrodynamic bearings
Allaire, P. E.; Flack, R. D.
1980-01-01
Two types of fixed pad hydrodynamic bearings (multilobe and pressure dam) were considered. Optimum and nonoptimum geometric configurations were tested. The optimum geometric configurations were determined by using a theoretical analysis and then the bearings were constructed for a flexible rotor test rig. It was found that optimizing bearings using this technique produces a 100% or greater increase in rotor stability. It is shown that this increase in rotor stability is carried out in the absence of certain types of instability mechanisms such as aerodynamic crosscoupling. However, the increase in rotor stability should greatly improve rotating machinery performance in the presence of such forces as well.
Influence of temperature and salinity on hydrodynamic forces
Directory of Open Access Journals (Sweden)
A. Escobar
2016-12-01
Full Text Available The purpose of this study is to introduce an innovative approach to offshore engineering so as to take variations in sea temperature and salinity into account in the calculation of hydrodynamic forces. With this in mind, a thorough critical analysis of the influence of sea temperature and salinity on hydrodynamic forces on piles like those used nowadays in offshore wind farms will be carried out. This influence on hydrodynamic forces occurs through a change in water density and viscosity due to temperature and salinity variation. Therefore, the aim here is to observe whether models currently used to estimate wave forces on piles are valid for different ranges of sea temperature and salinity apart from observing the limit when diffraction or nonlinear effects arise combining both effects with the magnitude of the pile diameter. Hence, specific software has been developed to simulate equations in fluid mechanics taking into account nonlinear and diffraction effects. This software enables wave produced forces on a cylinder supported on the sea bed to be calculated. The study includes observations on the calculation model's sensitivity as to a variation in the cylinder's diameter, on the one hand and, on the other, as to temperature and salinity variation. This software will enable an iterative calculation to be made for finding out the shape the pressure wave caused when a wave passes over will have for different pile diameters and water with different temperature and salinity.
Simulation of seismic signals from asymmetric LANL hydrodynamic calculations
International Nuclear Information System (INIS)
Stevens, J.L.; Rimer, N.; Halda, E.J.; Barker, T.G.; Davis, C.G.; Johnson, W.E.
1993-01-01
Hydrodynamic calculations of an asymmetric nuclear explosion source were propagated to teleseismic distances to investigate the effects of the asymmetric source on seismic signals. The source is an explosion in a 12 meter long canister with the device at one end of the canister and a metal plate adjacent to the explosion. This produces a strongly asymmetric two-lobed source in the hydrodynamic region. The hydrodynamic source is propagated to the far field using a three-step process. The Eulerian hydrodynamic code SOIL was used by LANL to calculate the material velocity, density, and internal energy up to a time of 8.9 milliseconds after the explosion. These quantities were then transferred to an initial grid for the Lagrangian elastic/plastic finite difference code CRAM, which was used by S-CUBED to propagate the signal through the region of nonlinear deformation into the external elastic region. The cavity size and shape at the time of the overlay were determined by searching for a rapid density change in the SOIL grid, and this interior region was then rezoned into a single zone. The CRAM calculation includes material strength and gravity, and includes the effect of the free surface above the explosion. Finally, far field body waves were calculated by integrating over a closed surface in the elastic region and using the representation theorem. A second calculation was performed using an initially spherical source for comparison with the asymmetric calculation
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...
Mix and hydrodynamic instabilities on NIF
Smalyuk, V. A.; Robey, H. F.; Casey, D. T.; Clark, D. S.; Döppner, T.; Haan, S. W.; Hammel, B. A.; MacPhee, A. G.; Martinez, D.; Milovich, J. L.; Peterson, J. L.; Pickworth, L.; Pino, J. E.; Raman, K.; Tipton, R.; Weber, C. R.; Baker, K. L.; Bachmann, B.; Berzak Hopkins, L. F.; Bond, E.; Caggiano, J. A.; Callahan, D. A.; Celliers, P. M.; Cerjan, C.; Dixit, S. N.; Edwards, M. J.; Felker, S.; Field, J. E.; Fittinghoff, D. N.; Gharibyan, N.; Grim, G. P.; Hamza, A. V.; Hatarik, R.; Hohenberger, M.; Hsing, W. W.; Hurricane, O. A.; Jancaitis, K. S.; Jones, O. S.; Khan, S.; Kroll, J. J.; Lafortune, K. N.; Landen, O. L.; Ma, T.; MacGowan, B. J.; Masse, L.; Moore, A. S.; Nagel, S. R.; Nikroo, A.; Pak, A.; Patel, P. K.; Remington, B. A.; Sayre, D. B.; Spears, B. K.; Stadermann, M.; Tommasini, R.; Widmayer, C. C.; Yeamans, C. B.; Crippen, J.; Farrell, M.; Giraldez, E.; Rice, N.; Wilde, C. H.; Volegov, P. L.; Gatu Johnson, M.
2017-06-01
Several new platforms have been developed to experimentally measure hydrodynamic instabilities in all phases of indirect-drive, inertial confinement fusion implosions on National Ignition Facility. At the ablation front, instability growth of pre-imposed modulations was measured with a face-on, x-ray radiography platform in the linear regime using the Hydrodynamic Growth Radiography (HGR) platform. Modulation growth of "native roughness" modulations and engineering features (fill tubes and capsule support membranes) were measured in conditions relevant to layered DT implosions. A new experimental platform was developed to measure instability growth at the ablator-ice interface. In the deceleration phase of implosions, several experimental platforms were developed to measure both low-mode asymmetries and high-mode perturbations near peak compression with x-ray and nuclear techniques. In one innovative technique, the self-emission from the hot spot was enhanced with argon dopant to "self-backlight" the shell in-flight. To stabilize instability growth, new "adiabat-shaping" techniques were developed using the HGR platform and applied in layered DT implosions.
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
Numerical Hydrodynamics in Special Relativity
Directory of Open Access Journals (Sweden)
Martí José Maria
2003-01-01
Full Text Available This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD. Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.
Soliton Gases and Generalized Hydrodynamics
Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien
2018-01-01
We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.
Anomalous hydrodynamics of Weyl materials
Monteiro, Gustavo; Abanov, Alexander
Kinetic theory is a useful tool to study transport in Weyl materials when the band-touching points are hidden inside a Fermi surface. It accounts, for example, for the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations (SdH effect) in the magnetoresistance together within the same framework. As an alternative approach to kinetic theory we also consider the regime of strong interactions where hydrodynamics can be applicable. A variational principle of these hydrodynamic equations can be found in and provide a natural framework to study hydrodynamic surface modes which correspond to the strongly-interacting physics signature of Fermi arcs. G.M. acknowledges the financial support from FAPESP.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Annual Report 2006 for Hydrodynamics and Radiation Hydrodynamics with Astrophysical Applications
Energy Technology Data Exchange (ETDEWEB)
R. Paul Drake
2007-04-05
We report the ongoing work of our group in hydrodynamics and radiation hydrodynamics with astrophysical applications. During the period of the existing grant, we have carried out two types of experiments at the Omega laser. One set of experiments has studied radiatively collapsing shocks, obtaining data using a backlit pinhole with a 100 ps backlighter and beginning to develop the ability to look into the shock tube with optical or x-ray diagnostics. Other experiments have studied the deeply nonlinear development of the Rayleigh-Taylor (RT) instability from complex initial conditions, using dual-axis radiographic data with backlit pinholes and ungated detectors to complete the data set for a Ph.D. student. We lead a team that is developing a proposal for experiments at the National Ignition Facility and are involved in experiments at NIKE and LIL. All these experiments have applications to astrophysics, discussed in the corresponding papers. We assemble the targets for the experiments at Michigan, where we also prepare many of the simple components. We also have several projects underway in our laboratory involving our x-ray source. The above activities, in addition to a variety of data analysis and design projects, provide good experience for graduate and undergraduates students. In the process of doing this research we have built a research group that uses such work to train junior scientists.
International Nuclear Information System (INIS)
R. Paul Drake
2007-01-01
We report the ongoing work of our group in hydrodynamics and radiation hydrodynamics with astrophysical applications. During the period of the existing grant, we have carried out two types of experiments at the Omega laser. One set of experiments has studied radiatively collapsing shocks, obtaining data using a backlit pinhole with a 100 ps backlighter and beginning to develop the ability to look into the shock tube with optical or x-ray diagnostics. Other experiments have studied the deeply nonlinear development of the Rayleigh-Taylor (RT) instability from complex initial conditions, using dual-axis radiographic data with backlit pinholes and ungated detectors to complete the data set for a Ph.D. student. We lead a team that is developing a proposal for experiments at the National Ignition Facility and are involved in experiments at NIKE and LIL. All these experiments have applications to astrophysics, discussed in the corresponding papers. We assemble the targets for the experiments at Michigan, where we also prepare many of the simple components. We also have several projects underway in our laboratory involving our x-ray source. The above activities, in addition to a variety of data analysis and design projects, provide good experience for graduate and undergraduates students. In the process of doing this research we have built a research group that uses such work to train junior scientists
Anisotropic hydrodynamics: Motivation and methodology
Energy Technology Data Exchange (ETDEWEB)
Strickland, Michael
2014-06-15
In this proceedings contribution I review recent progress in our understanding of the bulk dynamics of relativistic systems that possess potentially large local rest frame momentum-space anisotropies. In order to deal with these momentum-space anisotropies, a reorganization of relativistic viscous hydrodynamics can be made around an anisotropic background, and the resulting dynamical framework has been dubbed “anisotropic hydrodynamics”. I also discuss expectations for the degree of momentum-space anisotropy of the quark–gluon plasma generated in relativistic heavy ion collisions at RHIC and LHC from second-order viscous hydrodynamics, strong-coupling approaches, and weak-coupling approaches.
DEFF Research Database (Denmark)
Kunstmann-Olsen, Casper; Hoyland, James; Rubahn, Horst-Günter
2012-01-01
Details of hydrodynamic focusing in a 2D microfluidic channel-junction are investigated experimentally and theoretically, especially the effect on the focusing width of volumetric flow ratio r between main and side channels, as well as angle θ between channels. A non-linear relationship is observ...
Hydrodynamic instabilities and coherent structures. Final technical report, 1990--1997
Energy Technology Data Exchange (ETDEWEB)
Frenkel, A.L.
1998-04-01
This project has had two related parts: (1) Nonlinear behavior of wavy film flows, and (2) Linear and nonlinear stability of space-time-periodic flows. In this project, the author has developed novel methods of perturbative derivations of evolution equations governing film flows. In particular, these methods allow one to obtain a priori parametric regions of validity for such approximate descriptions of the nonlinear film dynamics. The methods yield the most general evolution equations, thus eliminating the need for a new derivation every time a new parametric domain is considered (corresponding to one choice of the infinite number of possible different order-of-magnitude relations between the system parameters). New concepts were introduced to advance understanding of these matters. New evolution equations were derived, and their numerical solutions were worked out. The latter uncovered new and unexpected types of nonlinear dynamical phenomena, including particle-like interactions of localized coherent structures having emerged spontaneously and, under certain conditions, proceeding to self-organized process of formation of patterns with unprecedented (at least in fluid dynamics) complexity of order (in an intuitive sense). Exciting agreements were obtained with recent important real-life experiments performed by different groups of researchers. Large-scale instability of space-periodic flow has been studied in connection with such intriguing phenomena in hydrodynamic turbulence as inverse cascade of energy to--and negative eddy viscosity at--large scales of motion and self-organization of large-scale coherent structures. Certain results can be obtained by considering a statistical ensemble of flows such as in Lipscombe, Frenkel and ter Haar 91. However, the main thrust in this project has been the study of instability of deterministic viscous flows sustained by a periodic external forcing. Whereas time-independent flows were considered before, the author included
Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics
Directory of Open Access Journals (Sweden)
D. N. Popov
2017-01-01
Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.
Hydrodynamic instability of compressible fluid in porous medium
International Nuclear Information System (INIS)
Argal, Shraddha; Tiwari, Anita; Sharma, P K; Prajapati, R P
2014-01-01
The hydrodynamic Rayleigh -Taylor instability of two superposed compressible fluids in porous medium has been studied. The dispersion relation is derived for such a medium by using normal mode analysis. The RT instability is discussed for various simplified configuration. The effect of porosity and dynamic viscosity has been analyzed and it is observed that porosity and dynamic viscosity have stabilizing effect on the Rayleigh- Taylor instability of compressible fluids.
Updated Lagrangian formulation for corrected smooth particle hydrodynamics
Huerta, Antonio; Vidal Seguí, Yolanda; Bonet Carbonell, Javier
2006-01-01
Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization techn...
Hydrodynamical processes in planet-forming accretion disks
Lin, Min-Kai
Understanding the physics of accretion flows in circumstellar disk provides the foundation to any theory of planet formation. The last few years have witnessed dramatic a revision in the fundamental fluid dynamics of protoplanetary accretion disks. There is growing evidence that the key to answering some of the most pressing questions, such as the origin of disk turbulence, mass transport, and planetesimal formation, may lie within, and intimately linked to, purely hydrodynamical processes in protoplanetary disks. Recent studies, including those from the proposal team, have discovered and highlighted the significance of several new hydrodynamical instabilities in the planet-forming regions of these disks. These include, but not limited to: the vertical shear instability, active between 10 to 100 AU; the zombie vortex instability, operating in regions interior to about 1AU; and the convective over-stability at intermediate radii. Secondary Rossbywave and elliptic instabilities may also be triggered, feeding off the structures that emerge from the above primary instabilities. The result of these hydrodynamic processes range from small-scale turbulence that transports angular momentum, to large-scale vortices that concentrate dust particles and enhance planetesimal formation. Hydrodynamic processes pertain to a wide range of disk conditions, meaning that at least one of these processes are active at any given disk location and evolutionary epoch. This remains true even after planet formation, which affects their subsequent orbital evolution. Hydrodynamical processes also have direct observable consequences. For example, vortices have being invoked to explain recent ALMA images of asymmetric `dust-traps' in transition disks. Hydrodynamic activities thus play a crucial role at every stage of planet formation and disk evolution. We propose to develop theoretical models of the above hydrodynamic processes under physical disk conditions by properly accounting for disk
National Research Council Canada - National Science Library
Rassias, Themistocles M
1987-01-01
... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...
Multi-shocks generation and collapsing instabilities induced by competing nonlinearities
Crosta, Matteo
2012-01-01
We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.
Anomalous hydrodynamics in two dimensions
Indian Academy of Sciences (India)
Abstract. A new approach is presented to discuss two-dimensional hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. Also, a connection between response parameters and anomaly coefficients is discussed. These are new results which, ...
Hydrodynamics of spatially ordered superfluids
Stoof, H.T.C.; Mullen, K.; Wallin, M.; Girvin, S.M.
1996-01-01
We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there
Anomalous hydrodynamics in two dimensions
Indian Academy of Sciences (India)
2016-01-14
Jan 14, 2016 ... A new approach is presented to discuss two-dimensional hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. Also, a connection between response parameters and anomaly coefficients is discussed. These are new ...
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
Radiation hydrodynamics in the laboratory
International Nuclear Information System (INIS)
1985-12-01
This report contains a collection of five preprints devoted to the subject of laser induced phenomena of radiation hydrodynamics. These preprints cover approximately the contents of the presentations made by the MPQ experimental laser-plasma group at the 17th European Conference on Laser Interaction with Matter (ECLIM), Rome, November 18-22, 1985. (orig.)
Hydrodynamics of a quark droplet
DEFF Research Database (Denmark)
Bjerrum-Bohr, Johan J.; Mishustin, Igor N.; Døssing, Thomas
2012-01-01
We present a simple model of a multi-quark droplet evolution based on the hydrodynamical description. This model includes collective expansion of the droplet, effects of the vacuum pressure and surface tension. The hadron emission from the droplet is described following Weisskopf's statistical...
Hydrodynamic instabilities in inertial fusion
International Nuclear Information System (INIS)
Hoffman, N.M.
1994-01-01
This report discusses topics on hydrodynamics instabilities in inertial confinement: linear analysis of Rayleigh-Taylor instability; ablation-surface instability; bubble rise in late-stage Rayleigh-Taylor instability; and saturation and multimode interactions in intermediate-stage Rayleigh-Taylor instability
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Hypersonic flow past slender bodies in dispersive hydrodynamics
International Nuclear Information System (INIS)
El, G.A.; Khodorovskii, V.V.; Tyurina, A.V.
2004-01-01
The problem of two-dimensional steady hypersonic flow past a slender body is formulated for dispersive media. It is shown that for the hypersonic flow, the original 2+0 boundary-value problem is asymptotically equivalent to the 1+1 piston problem for the fully nonlinear flow in the same physical system, which allows one to take advantage of the analytic methods developed for one-dimensional systems. This type of equivalence, well known in ideal Euler gas dynamics, has not been established for dispersive hydrodynamics so far. Two examples pertaining to collisionless plasma dynamics are considered
Design optimization and probabilistic analysis of a hydrodynamic journal bearing
Liniecki, Alexander G.
1990-01-01
A nonlinear constrained optimization of a hydrodynamic bearing was performed yielding three main variables: radial clearance, bearing length to diameter ratio, and lubricating oil viscosity. As an objective function a combined model of temperature rise and oil supply has been adopted. The optimized model of the bearing has been simulated for population of 1000 cases using Monte Carlo statistical method. It appeared that the so called 'optimal solution' generated more than 50 percent of failed bearings, because their minimum oil film thickness violated stipulated minimum constraint value. As a remedy change of oil viscosity is suggested after several sensitivities of variables have been investigated.
Mao, Yanbing; Zhang, Hongbin
2014-05-01
This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov-Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
Hydrodynamic Limit of Multiple SLE
Hotta, Ikkei; Katori, Makoto
2018-04-01
Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm-Loewner evolution (SLE) as the number of slits N goes to infinity. When the N slits grow from points on the real line R in a simultaneous way and go to infinity within the upper half plane H, an ordinary differential equation describing time evolution of the conformal map g_t(z) was derived in the N → ∞ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on R studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner's semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner's semicircle law determines the time evolution of the SLE hull, K_t \\subset H\\cup R, in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from -a < 0, and determine the multiple SLE in the hydrodynamic limit. After reporting these exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull K_t in the hydrodynamic limit.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
An implicit Smooth Particle Hydrodynamic code
Energy Technology Data Exchange (ETDEWEB)
Knapp, Charles E. [Univ. of New Mexico, Albuquerque, NM (United States)
2000-05-01
An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2017-12-01
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
2016-07-01
architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the
Hydrodynamics of vertical jumping in Archer fish
Techet, Alexandra H.; Mendelson, Leah
2017-11-01
Vertical jumping for aerial prey from an aquatic environment requires both propulsive power and precise aim to succeed. Rapid acceleration to a ballistic velocity sufficient for reaching the prey height occurs before the fish leaves the water completely and experiences a thousandfold drop in force-producing ability. In addition to speed, accuracy and stability are crucial for successful feeding by jumping. This talk examines the physics of jumping using the archer fish as a model. Better known for their spitting abilities, archer fish will jump multiple body lengths out of the water for prey capture, from a stationary position just below the free surface. Modulation of oscillatory body kinematics and use of multiple fins for force production are identified as methods through which the fish can meet requirements for both acceleration and stabilization in limited space. Quantitative 3D PIV wake measurements reveal how variations in tail kinematics relate to thrust production throughout the course of a jumping maneuver and over a range of jump heights. By performing measurements in 3D, the timing, interactions, and relative contributions to thrust and lateral forces from each fin can be evaluated, elucidating the complex hydrodynamics that enable archer fish water exit.
Hydrodynamics from Landau initial conditions
Energy Technology Data Exchange (ETDEWEB)
Sen, Abhisek [University of Tennessee, Knoxville (UTK); Gerhard, Jochen [Frankfurt Institute for Advanced Studies (FIAS), Germany; Torrieri, Giorgio [Universidade Estadual de Campinas, Instituto de Física " Gleb Wataghin" (IFGW), Sao Paulo, Brazil; Read jr, Kenneth F. [University of Tennessee (UTK) and Oak Ridge National Laboratory (ORNL); Wong, Cheuk-Yin [ORNL
2015-01-01
We investigate ideal hydrodynamic evolution, with Landau initial conditions, both in a semi-analytical 1+1D approach and in a numerical code incorporating event-by-event variation with many events and transverse density inhomogeneities. The object of the calculation is to test how fast would a Landau initial condition transition to a commonly used boost-invariant expansion. We show that the transition to boost-invariant flow occurs too late for realistic setups, with corrections of O (20 - 30%) expected at freezeout for most scenarios. Moreover, the deviation from boost-invariance is correlated with both transverse flow and elliptic flow, with the more highly transversely flowing regions also showing the most violation of boost invariance. Therefore, if longitudinal flow is not fully developed at the early stages of heavy ion collisions, 2+1 dimensional hydrodynamics is inadequate to extract transport coefficients of the quark-gluon plasma. Based on [1, 2
Hydrodynamic simulations of expanding shells
Czech Academy of Sciences Publication Activity Database
Wünsch, Richard; Palouš, Jan; Ehlerová, Soňa
2004-01-01
Roč. 289, 3-4 (2004), s. 35-36 ISSN 0004-640X. [From observation to self-consistent modelling of the ISM in galaxies. Porto, 03.09.2002-05.09.2002] R&D Projects: GA AV ČR KSK1048102 Keywords : hydrodynamic simulations * ISM * star formation Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 0.597, year: 2004
Hydrodynamics of spatially ordered superfluids
Energy Technology Data Exchange (ETDEWEB)
Stoof, H.T. [Institute for Theoretical Physics, University of Utrecht, Princetonplein 5, P.O. Box 80.006, 3508 TA Utrecht (The Netherlands); Mullen, K. [Department of Physics, University of Oklahoma, Norman, Oklahoma 73019-0225 (United States); Wallin, M. [Department of Theoretical Physics, Royal Institute of Technology, S-100 44 Stockholm (Sweden); Girvin, S.M. [Department of Physics, Indiana University, Bloomington, Indiana 47405 (United States)
1996-03-01
We derive the hydrodynamic equations for the supersolid and superhexatic phases of a neutral two-dimensional Bose fluid. We find, assuming that the normal part of the fluid is clamped to an underlying substrate, that both phases can sustain third-sound modes and that in the supersolid phase there are additional modes due to the superfluid motion of point defects (vacancies and interstitials). {copyright} {ital 1996 The American Physical Society.}
Particle hydrodynamics with tessellation techniques
Heß, Steffen; Springel, Volker
2010-08-01
Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. We find that the new `Voronoi Particle Hydrodynamics' (VPH) described here produces comparable results to SPH in shocks, and better ones in turbulent regimes of pure hydrodynamical simulations. We also discuss formulations of the artificial viscosity needed in this scheme and how judiciously chosen correction forces can be derived in order to maintain a high degree of particle order and hence a regular Voronoi mesh. This is especially helpful in simulating self-gravitating fluids with existing gravity solvers used for N-body simulations.
Numerical Hydrodynamics in Special Relativity.
Martí, José Maria; Müller, Ewald
2003-01-01
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction. Supplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.
Hydrodynamic description of spin Calogero-Sutherland model
Abanov, Alexander; Kulkarni, Manas; Franchini, Fabio
2009-03-01
We study a non-linear collective field theory for an integrable spin-Calogero-Sutherland model. The hydrodynamic description of this SU(2) model in terms of charge density, charge velocity and spin currents is used to study non-perturbative solutions (solitons) and examine their correspondence with known quantum numbers of elementary excitations [1]. A conventional linear bosonization or harmonic approximation is not sufficient to describe, for example, the physics of spin-charge (non)separation. Therefore, we need this new collective bosonic field description that captures the effects of the band curvature. In the strong coupling limit [2] this model reduces to integrable SU(2) Haldane-Shastry model. We study a non-linear coupling of left and right spin currents which form a Kac-Moody algebra. Our quantum hydrodynamic description for the spin case is an extension for the one found in the spinless version in [3].[3pt] [1] Y. Kato,T. Yamamoto, and M. Arikawa, J. Phys. Soc. Jpn. 66, 1954-1961 (1997).[0pt] [2] A. Polychronakos, Phys Rev Lett. 70,2329-2331(1993).[0pt] [3] A.G.Abanov and P.B. Wiegmann, Phys Rev Lett 95, 076402(2005)
Soliton shock wave fronts and self-similar discontinuities in dispersion hydrodynamics
International Nuclear Information System (INIS)
Gurevich, A.V.; Meshcherkin, A.P.
1987-01-01
Nonlinear flows in nondissipative dispersion hydrodynamics are examined. It is demonstrated that in order to describe such flows it is necessary to incorporate a new concept: a special discontinuity called a ''self-similar'' discontinuity consisting of a nondissipative shock wave and a powerful slow wave discontinuity in regular hydrodynamics. The ''self similar discontinuity'' expands linearly over time. It is demonstrated that this concept may be introduced in a solution to Euler equations. The boundary conditions of the ''self similar discontinuity'' that allow closure of Euler equations for dispersion hydrodynamics are formulated, i.e., those that replace the shock adiabatic curve of standard dissipative hydrodynamics. The structure of the soliton front and of the trailing edge of the shock wave is investigated. A classification and complete solution are given to the problem of the decay of random initial discontinuities in the hydrodynamics of highly nonisothermic plasma. A solution is derived to the problem of the decay of initial discontinuities in the hydrodynamics of magnetized plasma. It is demonstrated that in this plasma, a feature of current density arises at the point of soliton inversion
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws......Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Constructing higher-order hydrodynamics: The third order
Grozdanov, Sašo; Kaplis, Nikolaos
2016-03-01
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the N =4 supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.
Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics
Guercilena, Federico; Radice, David; Rezzolla, Luciano
2017-07-01
We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Hadron–Quark Combustion as a Nonlinear, Dynamical System
Directory of Open Access Journals (Sweden)
Amir Ouyed
2018-03-01
Full Text Available The hadron–quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron–quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.
Hadron–Quark Combustion as a Nonlinear, Dynamical System
Ouyed, Amir; Ouyed, Rachid; Jaikumar, Prashanth
2018-03-01
The hadron-quark combustion front is a system that couples various processes, such as chemical reactions, hydrodynamics, diffusion, and neutrino transport. Previous numerical work has shown that this system is very nonlinear, and can be very sensitive to some of these processes. In these proceedings, we contextualize the hadron-quark combustion as a nonlinear system, subject to dramatic feedback triggered by leptonic weak decays and neutrino transport.
Disruptive Innovation in Numerical Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Waltz, Jacob I. [Los Alamos National Laboratory
2012-09-06
We propose the research and development of a high-fidelity hydrodynamic algorithm for tetrahedral meshes that will lead to a disruptive innovation in the numerical modeling of Laboratory problems. Our proposed innovation has the potential to reduce turnaround time by orders of magnitude relative to Advanced Simulation and Computing (ASC) codes; reduce simulation setup costs by millions of dollars per year; and effectively leverage Graphics Processing Unit (GPU) and future Exascale computing hardware. If successful, this work will lead to a dramatic leap forward in the Laboratory's quest for a predictive simulation capability.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2000-05-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinearity management and diffraction management for the ...
Indian Academy of Sciences (India)
Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.
Hydrodynamics and stellar winds an introduction
Maciel, Walter J
2014-01-01
Stellar winds are a common phenomenon in the life of stars, from the dwarfs like the Sun to the red giants and hot supergiants, constituting one of the basic aspects of modern astrophysics. Stellar winds are a hydrodynamic phenomenon in which circumstellar gases expand towards the interstellar medium. This book presents an elementary introduction to the fundamentals of hydrodynamics with an application to the study of stellar winds. The principles of hydrodynamics have many other applications, so that the book can be used as an introduction to hydrodynamics for students of physics, astrophysics and other related areas.
International Nuclear Information System (INIS)
Montano-Ley, Y.; Peraza-Vizcarra, R.; Paez-Osuna, F.
2007-01-01
The tidal hydrodynamics of the Topolobampo coastal lagoon system (Mexico) has been investigated through a modified two dimensional non-linear hydrodynamic finite difference model. The advective and diffusive process acting over a hypothetical pollutant released into the coastal lagoon have also been simulated. Maxima tidal currents (0.85 m/s) were predicted within the main channel, in agree with direct measurements. The direction of the observed fastest currents (SW), also agree quite well with the direction of the strongest tidal current predicted in this investigation, which occur during the ebb when the water of the coastal lagoon is discharged into the Gulf of California. Residual currents (0.01-0.05 m/s) were also predicted. The hypothetical pollutant released within the Topolobampo Harbor would spread to both Ohuira and Topolobampo sections, reaching the inlet after approximately 12 days. - A model has been developed to simulate the tidal hydrodynamics and the behavior of a pollutant in the Topolobampo lagoon
Nonlinear Markov processes: Deterministic case
International Nuclear Information System (INIS)
Frank, T.D.
2008-01-01
Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution
Hydrodynamic dispersion within porous biofilms.
Davit, Y; Byrne, H; Osborne, J; Pitt-Francis, J; Gavaghan, D; Quintard, M
2013-01-01
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.
International Nuclear Information System (INIS)
Ferapontov, E.V.
2002-01-01
Hydrodynamic surfaces are solutions of hydrodynamic-type systems viewed as non-parametrized submanifolds of the hodograph space. We propose an invariant differential-geometric characterization of hydrodynamic surfaces by expressing the curvature form of the characteristic web in terms of the reciprocal invariants. (author)
4th International Conference on Structural Nonlinear Dynamics and Diagnosis
2018-01-01
This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...
Capture and confinement of solitons in nonlinear integrable systems
International Nuclear Information System (INIS)
Mel'nikov, V.K.
1988-01-01
Some nonlinear integrable systems were found to have solutions describing solitons that come from infinity and then are captured into oscillatory regimes. These solutions were obtained by the inverse scattering method for the one-dimensional Schroedinger operator on a straight line. The obtained results are relevant to some problems of hydrodynamics, plasma physics, solid state physics, etc. 2 refs
Breathers and rogue waves: Demonstration with coupled nonlinear ...
Indian Academy of Sciences (India)
Abstract. Different types of breathers and rogue waves (RWs) are some of the important coher- ent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non- linear Schrödinger (NLS) ...
Weakly nonlinear analysis of two dimensional sheared granular flow
Saitoh, K.; Hayakawa, Hisao
2011-01-01
Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg–Landau equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the
On short wave stability and sufficient conditions for stability in the ...
Indian Academy of Sciences (India)
We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. We prove a short wave stability result, namely, if k > 0 is the wave number of a normal mode then k > k c (for some critical wave number k c ) implies the ...
The hydrodynamic description of pseudorapidity distributions at ...
Indian Academy of Sciences (India)
2017-03-15
Mar 15, 2017 ... hard to solve them analytically. From this point of view, hydrodynamics is tremendously complicated. This is the reason why from the time of ... erful calculation system, sophisticated skills are also needed for avoiding instabilities in solving partial dif- ferential hydrodynamic equations. Furthermore, as the.
Two-fluid hydrodynamic model for semiconductors
DEFF Research Database (Denmark)
Maack, Johan Rosenkrantz; Mortensen, N. Asger; Wubs, Martijn
2018-01-01
The hydrodynamic Drude model (HDM) has been successful in describing the optical properties of metallic nanostructures, but for semiconductors where several different kinds of charge carriers are present an extended theory is required. We present a two-fluid hydrodynamic model for semiconductors...
Kotnik, Jože; Žagar, Dušan; Rajar, Rudi; Horvat, Milena
2004-01-01
PCFLOW3D - a three-dimensional mathematical model that was developed at the Chair of Fluid Mechanics of the Faculty of Civil and Geodetic Engineering, University of Ljubljana, was used for hydrodynamic and Hg transport simulations in Lake Velenje. The model is fully non-linear and computes three velocity components, water elevation and pressure. Transport-dispersion equations for salinity and heat (and/or any pollutant) are further used to compute the distributions of these par...
Effect of Surface Roughness on Hydrodynamic Bearings
Majumdar, B. C.; Hamrock, B. J.
1981-01-01
A theoretical analysis on the performance of hydrodynamic oil bearings is made considering surface roughness effect. The hydrodynamic as well as asperity contact load is found. The contact pressure was calculated with the assumption that the surface height distribution was Gaussian. The average Reynolds equation of partially lubricated surface was used to calculate hydrodynamic load. An analytical expression for average gap was found and was introduced to modify the average Reynolds equation. The resulting boundary value problem was then solved numerically by finite difference methods using the method of successive over relaxation. The pressure distribution and hydrodynamic load capacity of plane slider and journal bearings were calculated for various design data. The effects of attitude and roughness of surface on the bearing performance were shown. The results are compared with similar available solution of rough surface bearings. It is shown that: (1) the contribution of contact load is not significant; and (2) the hydrodynamic and contact load increase with surface roughness.