Relevant bibliographies by topics / Instability exponential equation

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Academic literature on the topic 'Instability exponential equation'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Instability exponential equation"

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SCHEUTZOW, MICHAEL. "EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 05, no. 02 (2005): 163–74. http://dx.doi.org/10.1142/s0219493705001468.

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In this survey, we provide some tools to obtain estimates for the almost sure exponential growth rate of a stochastic delay differential equation (sdde) which fixes zero. In particular, we are interested in determining whether the solutions of a given sdde are exponentially stable (i.e. have a negative exponential growth rate) or not. We focus on equations without drift, which are a good testground to assess if a method is powerful enough to discriminate between stability and instability when a certain parameter (e.g. noise intensity) varies. The most powerful tool we provide is the method of
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Kalashnik, M. V. "Shear Flow Instability over a Finite Time Interval." Известия Российской академии наук. Физика атмосферы и океана 59, no. 2 (2023): 165–72. http://dx.doi.org/10.31857/s0002351523020037.

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Within the framework of a discrete quasi-geostrophic model with two vertical levels, the problem of linear stability of the flow of a stratified rotating fluid with constant vertical and horizontal velocity shifts is solved. It is shown that taking into account the horizontal shear leads to a qualitative change in the dynamics of unstable wave disturbances. The main feature is related to the effect of temporary exponential growth of unstable perturbations, i.e. growth over a finite time period. This effect manifests itself in the alternation of stages of smooth oscillating behavior (in time) w
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Mandache, Niculae. "Exponential instability in an inverse problem for the Schrödinger equation." Inverse Problems 17, no. 5 (2001): 1435–44. http://dx.doi.org/10.1088/0266-5611/17/5/313.

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Kuznetsov, V. D. "Magnetic Buoyancy with Viscosity and Ohmic Dissipation and Flux Tube Formation." Symposium - International Astronomical Union 142 (1990): 58–59. http://dx.doi.org/10.1017/s0074180900087726.

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In the framework of the magnetohydrodynamic equations with dissipative terms in the form of turbulent viscosity (Vt) the linear stage of the instability of a subphotospheric field with respect to magnetic buoyancy is considered. For an exponential in z, isothermal plane-parallel atmosphere with a constant Alfvenic velocity the perturbations of the form are described by differential equation with constant coefficients. The qualitative dependence of the growth rate of instability on transverse wave number is determined (see Figures 1 and 2) and characteristic scales of the magnetic tubes are eva
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Kosheleva, Elena. "On the Dynamic Stability of a Reinforced Concrete Plate, Taking into Account the Material Creep." MATEC Web of Conferences 196 (2018): 01025. http://dx.doi.org/10.1051/matecconf/201819601025.

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The problem of the dynamic stability of a reinforced concrete plate armoured in two directions parallel to its edges is considered. To describe the viscoelastic properties of concrete, an integral dependence was adopted with an exponential kernel. The use of this dependence led to a linear differential equation of plate vibration. In addition to the creep of concrete, the work of the reinforcement was taken into account. The solution of the differential equation of vibrations of a plate in the form of a series with separated variables is considered, which satisfies the plate fastening conditio
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Afful, Adusei-Poku, and Ernest Yankson. "Exponential stability and instability in nonlinear differential equations with multiple delays." Proyecciones (Antofagasta) 42, no. 3 (2023): 681–93. http://dx.doi.org/10.22199/issn.0717-6279-4197.

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Inequalities regarding the solutions of the nonlinear differential equation with multiple delays xl(t) = a(t)f(x(t)) +Σni=1bi(t)f(x(t − hi)), are obtained by means of Lyapunov functionals. These inequalities are then used to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the multi delay nonlinear differential equation. In addition, we obtain a criterion for the instability of the zero solution. The results generalizes some results in the literature.
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Kelleche, Abdelkarim, and Amirouche Berkani. "On exponential stabilization of a nonlinear neutral wave equation." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–10. http://dx.doi.org/10.5269/bspm.52132.

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This work aims to study a nonlinear wave equation subject to a delay of neutral type. The nonlinearity and the delay appear in the second time derivative. In spite of the fact that delays by nature, have an instability effect on the structures, the strong damping is sufficient to allow the system to reach its equilibrium state with an exponential manner. The difficulties arising from the nonlinearity have been overcome by using an inequality due to a Sobolev embedding theorem. The main result has been established without any condition on the coefficient of the neutral delay.
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Grimshaw, Roger. "Two-dimensional modulation instability of wind waves." Journal of Ocean Engineering and Marine Energy 5, no. 4 (2019): 413–17. http://dx.doi.org/10.1007/s40722-019-00146-7.

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Abstract It is widely known that deep-water waves are modulationally unstable and that this can be modelled by a nonlinear Schrödinger equation. In this paper, we extend the previous studies of the effect of wind forcing on this instability to water waves in finite depth and in two horizontal space dimensions. The principal finding is that the instability is enhanced and becomes super-exponential and that the domain of instability in the modulation wavenumber space is enlarged. Since the outcome of modulation instability is expected to be the generation of rogue waves, represented within the f
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SAANOUNI, T. "GLOBAL WELL-POSEDNESS AND INSTABILITY OF A NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL." Journal of the Australian Mathematical Society 98, no. 1 (2014): 78–103. http://dx.doi.org/10.1017/s1446788714000391.

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AbstractThis paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation with a harmonic potential and exponential growth nonlinearity in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing case, existence of nonglobal solutions is discussed via potential-well arguments.
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Deka, Pranab J., and Lukas Einkemmer. "Exponential Integrators for Resistive Magnetohydrodynamics: Matrix-free Leja Interpolation and Efficient Adaptive Time Stepping." Astrophysical Journal Supplement Series 259, no. 2 (2022): 57. http://dx.doi.org/10.3847/1538-4365/ac5177.

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Abstract We propose a novel algorithm for the temporal integration of the resistive magnetohydrodynamics (MHD) equations. The approach is based on exponential Rosenbrock schemes in combination with Leja interpolation. It naturally preserves Gauss’s law for magnetism and is unencumbered by the stability constraints observed for explicit methods. Remarkable progress has been achieved in designing exponential integrators and computing the required matrix functions efficiently. However, employing them in MHD simulations of realistic physical scenarios requires a matrix-free implementation. We show
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Book chapters on the topic "Instability exponential equation"

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Davani, Sina, and Ramazan Asmatulu. "Item Theoretical study on instability of the base solutions of Lorenz system via Ordinary Differential Equations." In Proceedings of the 2021 International IEMS Conference, March 15-16, 2021. Wichita State University, 2021. http://dx.doi.org/10.62704/10057/24725.

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The Lorenz system is well-known for producing chaotic solutions for a particular range of technical systems and process characteristics. To examine the instability, fluctuation parameters in the form of exponential functions are introduced to the base solutions of the ODEs, and numerical and computational methodologies are used to determine the range of values that cause instability under different conditions. This paper will focus on the Lorenz system's instability of Ordinary Differential Equations (ODE) that regulates the thermal-hydrodynamic behavior of a two-dimensional fluid layer which
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Easton, Robert W. "Examples." In Geometric Methods for Discrete Dynamical Systems. Oxford University PressNew York, NY, 1998. http://dx.doi.org/10.1093/oso/9780195085457.003.0001.

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Abstract A mathematical model of a physical system consists of a set which represents all “states” of the system together with a law which determines the time evolution of states. Part of a scientist’s job is to identify the relevant set of states and to propose the law which governs their evolution. For example, states for Newton’s model of the solar system consist of all positions and velocities of the sun and planets. The law of evolution is determined by a system of second-order differential equations. Newton’s model does not include effects due to the spins, oblateness, magnetic fields of
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Conference papers on the topic "Instability exponential equation"

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Rahimov, F. "Use of Eigenvalue Stability Analysis for Liner Inflow Test Interpretation." In SPE Advances in Integrated Reservoir Modelling and Field Development Conference and Exhibition. SPE, 2025. https://doi.org/10.2118/225392-ms.

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Summary The Well Integrity Management System is a central policy outlining well integrity requirements to ensure operational safety and safe production throughout well lifecycle. Among these requirements is a liner inflow test, particularly when set above the production packer to prevent any potential non-conformities such as Sustained Casing Pressure, tubular corrosion, an underground blowout and many other Well Integrity issues during production. Some Well Integrity Guidelines propose the use of Horner's technique to interpret these tests where predictions are made based on the Y-intercept o
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Cho, Jihyun, and Samuel F. Asokanthan. "Dynamic Stability of Ring-Based MEMS Gyroscopes." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85321.

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Dynamic stability of ring-based MEMS gyroscopes subjected to harmonic perturbations in input angular rate is examined using an asymptotic approach. The governing equations that represent the transverse and tangential in-plane motion of the ring are derived via Hamilton’s principle. The equations of motion, after discretization and suitable linearization, represent a two-degree-of-freedom time-varying linear gyroscopic system. Such a system can exhibit instability behaviour characterized by exponential growth in response amplitudes. Employing the method of averaging, conditions for instability
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Sanches, Leonardo, Guilhem Michon, Alain Berlioz, and Daniel Alazard. "Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71138.

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Recent works study the ground resonance in helicopters under the aging effects. Indeed, the blades lead-lag stiffness may vary randomly with time and be different from each other (i.e.: anisotropic rotor). The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon is determined through numerical investigations on the periodical equations of motion, treated by using Floquet’s theory. Stability chart highlights the appearance of new instability zones as function of the perturbation introduced on the lead-lag stiffness of one blade. In order to v
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Finnis, M. V., and A. Brown. "The Streamwise Development of Görtler Vortices in a Favorable Pressure Gradient." In ASME 1994 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/94-gt-166.

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Measurements are presented of the streamwise velocity variation within a laminar boundary layer on a concave surface of 4 m radius of curvature for which the free-stream velocity gradient factor ν/U02dU0/dx was approximately 1 × 10−6. The velocity variation was consistent with the presence of counter-rotating vortices resulting from the Görtler instability. The vortices exhibited exponential growth over the streamwise extent of the measurements to a disturbance amplitude of approximately 13% of the local freestream velocity. The vortex growth rates were found to be less than those for a zero v
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De Angelis, C., and M. Santagiustina. "Induced nonlinear modulational instability in high birefringence fibers: a quantitative study." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/nlgwp.1993.tub.6.

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Modulational instability (MI) refers to the growth of an initial weak perturbation at the expense of a plane wave in a dispersive or diffractive nonlinear medium [1]. In the context of optical fibers, temporal MI in the anomalous group-velocity dispersion (GVD) regime has been extensively studied in recent years for its potential application in high-repetition rate ultrashort pulse train generation [2] and ultrafast optical switching [3]. The domain of MI may be extended to the normal GVD regime by means of a feedback loop [4] or exploiting cross-phase modulation (XPM) [5,6]. In the latter cas
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Silva, Camilo F., Thomas Runte, Wolfgang Polifke, and Luca Magri. "Uncertainty Quantification of Growth Rates of Thermoacoustic Instability by an Adjoint Helmholtz Solver." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57659.

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The objective of this paper is to quantify uncertainties in thermoacoustic stability analysis with a Helmholtz solver and its adjoint. Thermoacoustic combustion instability may be described by the Helmholtz equation combined with a model for the flame dynamics. Typically, such a formulation leads to an eigenvalue problem in which the eigenvalue appears under nonlinear terms, such as exponentials related to time delays that result from the flame model. Consequently, the standard adjoint sensitivity formulation should be augmented by first- and second-order correction terms that account for the
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Li, Yuzhu, and David R. Fuhrman. "CFD Simulation of Nonlinear Deep-Water Wave Instabilities Involving Wave Breaking." In ASME 2021 40th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/omae2021-62805.

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Abstract Extreme waves at the sea surface can have severe impacts on marine structures. One of the theoretical mechanisms leading to extreme waves is the instability of deep-water wave trains subject to initially small perturbations, which then grow exponentially. The present study focuses on the two-dimensional Benjamin–Feir (or modulational) instability and the three-dimensional crescent (or horseshoe) waves, also known as Class I and Class II instabilities, respectively. Numerical studies on Class I and Class II wave instabilities to date have been limited to models founded on potential flo
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Ishihara, Abraham K., and Shahar Ben-Menahem. "A Matrix WKB Approach to Feedforward and Feedback Control." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-16119.

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We apply a powerful new analytical approximation method, recently developed by the authors, to the design and analysis of feedforward and feedback control systems. This formalism employs a matrix version of the WKB expansion, which is an asymptotic approximation method familiar in quantum mechanics and classical continuum mechanics. Our matrix WKB formalism has proven remarkably useful in approximating and characterizing the long-term dynamics of systems of ODEs (both linear and nonlinear) when there exists a time scale hierarchy. In particular, the linear error dynamics encountered in the ana
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Feng, Zhipeng, Huanhuan Qi, Xuan Huang, Guo Chen, Shuai Liu, and Yixiong Zhang. "Flow Induced Vibration and Fretting Wear Characteristics of Fuel Rods." In 2021 28th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/icone28-62135.

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Abstract Fuel assembly is located in the reactor core, which is the key component of nuclear power plant reactor. Its structural integrity will directly affect the safety and reliability of nuclear reactor operation. Fretting wear between fuel rod and grid supports caused by flow induced vibration is currently one of the main causes of fuel rod failure, which is also the most concerned phenomenon in fuel assembly design. Based on the random vibration theory and considering the interaction between fuel rod and support grid, a theoretical model and evaluation criteria for response prediction are
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Yu, Huan, Shumon Koga, and Miroslav Krstic. "Stabilization of Traffic Flow With a Leading Autonomous Vehicle." In ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dscc2018-9239.

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This paper develops boundary control law for autonomous vehicles to stabilize the stop-and-go traffic on freeway. The macroscopic traffic dynamics is described by the Aw-Rascle-Zhang (ARZ) model in a time and state dependent domain. The leading autonomous vehicle aims to regulate the traffic behind it to uniform equilibrium and the domain length of the traffic to a setpoint. The traffic density and speed is governed by second-order, nonlinear hyperbolic partial differential equations (PDEs), coupled with a state-dependent ODE for the leading autonomous vehicle. The actuation is the speed of au
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