Interfacial instabilities and Kapitsa pendula
Krieger, Madison
2015-11-01
Determining the critera for onset and amplitude growth of instabilities is one of the central problems of fluid mechanics. We develop a parallel between the Kapitsa effect, in which a pendulum subject to high-frequency low-amplitude vibrations becomes stable in the inverted position, and interfaces separating fluids of different density. It has long been known that such interfaces can be stabilized by vibrations, even when the denser fluid is on top. We demonstrate that the stability diagram for these fluid interfaces is identical to the stability diagram for an appopriate Kapitsa pendulum. We expand the robust, ``dictionary''-type relationship between Kapitsa pendula and interfacial instabilities by considering the classical Rayleigh-Taylor, Kelvin-Helmholtz and Plateau instabilities, as well as less-canonical examples ranging in scale from the micron to the width of a galaxy.
Interfacial instabilities in vibrated fluids
Porter, Jeff; Laverón-Simavilla, Ana; Tinao Perez-Miravete, Ignacio; Fernandez Fraile, Jose Javier
2016-07-01
Vibrations induce a range of different interfacial phenomena in fluid systems depending on the frequency and orientation of the forcing. With gravity, (large) interfaces are approximately flat and there is a qualitative difference between vertical and horizontal forcing. Sufficient vertical forcing produces subharmonic standing waves (Faraday waves) that extend over the whole interface. Horizontal forcing can excite both localized and extended interfacial phenomena. The vibrating solid boundaries act as wavemakers to excite traveling waves (or sloshing modes at low frequencies) but they also drive evanescent bulk modes whose oscillatory pressure gradient can parametrically excite subharmonic surface waves like cross-waves. Depending on the magnitude of the damping and the aspect ratio of the container, these locally generated surfaces waves may interact in the interior resulting in temporal modulation and other complex dynamics. In the case where the interface separates two fluids of different density in, for example, a rectangular container, the mass transfer due to vertical motion near the endwalls requires a counterflow in the interior region that can lead to a Kelvin-Helmholtz type instability and a ``frozen wave" pattern. In microgravity, the dominance of surface forces favors non-flat equilibrium configurations and the distinction between vertical and horizontal applied forcing can be lost. Hysteresis and multiplicity of solutions are more common, especially in non-wetting systems where disconnected (partial) volumes of fluid can be established. Furthermore, the vibrational field contributes a dynamic pressure term that competes with surface tension to select the (time averaged) shape of the surface. These new (quasi-static) surface configurations, known as vibroequilibria, can differ substantially from the hydrostatic state. There is a tendency for the interface to orient perpendicular to the vibrational axis and, in some cases, a bulge or cavity is induced
Interfacial Instabilities in Evaporating Drops
Moffat, Ross; Sefiane, Khellil; Matar, Omar
2007-11-01
We study the effect of substrate thermal properties on the evaporation of sessile drops of various liquids. An infra-red imaging technique was used to record the interfacial temperature. This technique illustrates the non-uniformity in interfacial temperature distribution that characterises the evaporation process. Our results also demonstrate that the evaporation of methanol droplets is accompanied by the formation of wave-trains in the interfacial temperature field; similar patterns, however, were not observed in the case of water droplets. More complex patterns are observed for FC-72 refrigerant drops. The effect of substrate thermal conductivity on the structure of the complex pattern formation is also elucidated.
Nonlinear helical MHD instability
Energy Technology Data Exchange (ETDEWEB)
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Interfacial Instability during Granular Erosion.
Lefebvre, Gautier; Merceron, Aymeric; Jop, Pierre
2016-02-12
The complex interplay between the topography and the erosion and deposition phenomena is a key feature to model granular flows such as landslides. Here, we investigated the instability that develops during the erosion of a wet granular pile by a dry dense granular flow. The morphology and the propagation of the generated steps are analyzed in relation to the specific erosion mechanism. The selected flowing angle of the confined flow on a dry heap appears to play an important role both in the final state of the experiment, and for the shape of the structures. We show that the development of the instability is governed by the inertia of the flow through the Froude number. We model this instability and predict growth rates that are in agreement with the experiment results.
Polygonal instabilities on interfacial vorticities
Labousse, Matthieu
2015-01-01
We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.
Nonlinear Instability of Liquid Layers.
Newhouse, Lori Ann
The nonlinear instability of two superposed viscous liquid layers in planar and axisymmetric configurations is investigated. In the planar configuration, the light layer fluid is bounded below by a wall and above by a heavy semiinfinite fluid. Gravity drives the instability. In the first axisymmetric configuration, the layer is confined between a cylindrical wall and a core of another fluid. In the second, a thread is suspended in an infinite fluid. Surface tension forces drive the instability in the axisymmetric configurations. The nonlinear evolution of the fluid-fluid interface is computed for layers of arbitrary thickness when their dynamics are fully coupled to those of the second fluid. Under the assumption of creeping flow, the flow field is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind for the strength of the distribution is derived and then solved using an iterative technique. The Green's functions produce flow fields which are periodic in the direction parallel to the wall and have zero velocity on the wall. For small and moderate surface tension, planar layers evolve into a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of the plumes depends on the surface tension and the ratio of the fluid viscosities. As the viscosity of the layer increases, the plumes change from a well defined drop on top of a narrow stem to a compact column of rising fluid. The capillary instability of cylindrical interfaces and interfaces in which the core thickness varies in the axial direction are investigated. In both the unbounded and wall bounded configurations, the core evolves into a periodic array of elongated fluid drops connected by thin, almost cylindrical fluid links. The characteristics of the drop-link structure depend on the core thickness, the ratio of the core radius to the wall radius, and the ratio of the fluid viscosities. The factors controlling the
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Interfacial fluid instabilities and Kapitsa pendula
Krieger, Madison Ski
2015-01-01
The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilised by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum, we demonstrate how stability can be induced in fluid systems by properly tuned vibrations. We construct a "dictionary"-type relationship between various pendula and the classical Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational instabilities. This makes several results in control theory and dynamical systems directly applicable to the study of "tunable" fluid instabilities, where the critical wavelength depends on the e...
Wettability controls slow immiscible displacement through local interfacial instabilities
Jung, Michael; Brinkmann, Martin; Seemann, Ralf; Hiller, Thomas; Sanchez de La Lama, Marta; Herminghaus, Stephan
2016-11-01
Immiscible fluid displacement with average front velocities in the capillary-dominated regime is studied in a transparent Hele-Shaw cell with cylindrical posts. Employing various combinations of fluids and wall materials allows us to cover a range of advancing contact angles 46∘≤θa≤180∘ of the invading fluid in our experiments. In parallel, we study the displacement process in particle-based simulations that account for wall wettability. Considering the same arrangement of posts in experiments and simulation, we find a consistent crossover between stable interfacial displacement at θa≲80∘ and capillary fingering at high contact angles θa≳120∘ . The position of the crossover is quantified through the evolution of the interface length and the final saturation of the displaced fluid. A statistical analysis of the local displacement processes demonstrates that the shape evolution of the fluid front is governed by local instabilities as proposed by Cieplak and Robbins for a quasistatic interfacial displacement [Cieplak and Robbins, Phys. Rev. Lett. 60, 2042 (1988), 10.1103/PhysRevLett.60.2042]. The regime of stable front advances coincides with a corresponding region of contact angles where cooperative interfacial instabilities prevail. Capillary fingering, however, is observed only for large θa, where noncooperative instabilities dominate the invasion process.
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability o...
Institute of Scientific and Technical Information of China (English)
Kadry Zakaria; Magdy A.Sirwah; Ahmed Assaf
2008-01-01
The problem of nonlinear instability of interfa-cial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The sys-tem is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solv-ability conditions, which are used to construct like-nonlinear Schrodinger equations (1-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret-ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appear-ance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the non-linear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.
Lessons Learned from Numerical Simulations of Interfacial Instabilities
Cook, Andrew
2015-11-01
Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM) and Kelvin-Helmholtz (KH) instabilities serve as efficient mixing mechanisms in a wide variety of flows, from supernovae to jet engines. Over the past decade, we have used the Miranda code to temporally integrate the multi-component Navier-Stokes equations at spatial resolutions up to 29 billion grid points. The code employs 10th-order compact schemes for spatial derivatives, combined with 4th-order Runge-Kutta time advancement. Some of our major findings are as follows: The rate of growth of a mixing layer is equivalent to the net mass flux through the equi-molar plane. RT growth rates can be significantly reduced by adding shear. RT instability can produce shock waves. The growth rate of RM instability can be predicted from known interfacial perturbations. RM vortex projectiles can far outrun the mixing region. Thermal fluctuations in molecular dynamics simulations can seed instabilities along the braids in KH instability. And finally, enthalpy diffusion is essential in preserving the second law of thermodynamics. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Interfacial Instabilities Driven by Self-Gravity in the ISM: Onset and Evolution
Hueckstaedt, R. M.; Hunter, J. H., Jr.
2000-12-01
As the sites of all present day star formation within the Milky Way, cold molecular clouds are a vital link in the evolution of tenuous interstellar gas into stars. Any comprehensive theory of star formation must include a study of the hydrodynamic processes that effect molecular cloud morphology. In the ISM, hydrodynamic instabilities and turbulence play large roles in shaping clouds and creating regions capable of gravitational collapse. One of the key forces in the interstellar environment is self-gravity. Regardless of the mechanism initially responsible for creating density enhancements, self-gravity must ultimately drive the final collapse. A recent study has shown that self-gravity also gives rise to an interfacial instability that persists in the static limit when a density discontinuity exists (Hunter, Whitaker & Lovelace 1997). This instability also persists in the absence of a constant gravitational acceleration, unlike the familiar Rayleigh-Taylor instability. Analytic studies in Cartesian geometry predict that for perturbations proportional to exp(-iωt), the instability has an incompressible growth rate ω2= -2πG(ρ 1-ρ 2)2/(ρ1+ρ2). The growth rate is independent of the perturbation wavelength. Studies have also included cases in cylindrical geometry in which a static density interface has proven stable to kink modes but unstable to sausage modes. In the case of sausage modes, (perturbations in the radial direction), there exists a critical wavelength below which the instability does not appear. In this paper, we present two-dimensional numerical models designed to examine this self-gravity driven instability. A hydrodynamic code with self-gravity is used to test the analytic predictions in Cartesian and cylindrical geometries and to follow the instability into the nonlinear regime. We consider how the growth of hydrodynamic instabilities, including self-gravity driven instabilities, can have a role in shaping the ISM. We discuss implications for
3-D nonlinear evolution of MHD instabilities
Energy Technology Data Exchange (ETDEWEB)
Bateman, G.; Hicks, H. R.; Wooten, J. W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed.
Manipulation of interfacial instabilities by using a soft, deformable solid layer
Indian Academy of Sciences (India)
Gaurav; V Shankar
2015-05-01
Multilayer flows are oftensusceptible to interfacial instabilities caused due to jump in viscosity/elasticity across thefluid–fluid interface. It is frequently required to manipulate and control these interfacial instabilities in various applications such as coating processes or polymer coextrusion. We demonstrate here the possibility of using a deformable solid coating to control such interfacial instabilities for various flow configurations and for different fluid rheological behaviors. In particular, we show complete suppression of interfacial flow instabilities by making the walls sufficiently deformable when the configuration was otherwise unstable for the case of flow past a rigid surface. While these interfacial instabilities could be suppressed in certain parameter regimes, it is also possible to enhance the flow instabilities by tuning the shear modulus of the deformable solid coating for other ranges of parameters.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Interfacial instabilities in a stratified flow of two superposed fluids
Schaflinger, Uwe
1994-06-01
Here we shall present a linear stability analysis of a laminar, stratified flow of two superposed fluids which are a clear liquid and a suspension of solid particles. The investigation is based upon the assumption that the concentration remains constant within the suspension layer. Even for moderate flow-rates the base-state results for a shear induced resuspension flow justify the latter assumption. The numerical solutions display the existence of two different branches that contribute to convective instability: long and short waves which coexist in a certain range of parameters. Also, a range exists where the flow is absolutely unstable. That means a convectively unstable resuspension flow can be only observed for Reynolds numbers larger than a lower, critical Reynolds number but still smaller than a second critical Reynolds number. For flow rates which give rise to a Reynolds number larger than the second critical Reynolds number, the flow is absolutely unstable. In some cases, however, there exists a third bound beyond that the flow is convectively unstable again. Experiments show the same phenomena: for small flow-rates short waves were usually observed but occasionally also the coexistence of short and long waves. These findings are qualitatively in good agreement with the linear stability analysis. Larger flow-rates in the range of the second critical Reynolds number yield strong interfacial waves with wave breaking and detached particles. In this range, the measured flow-parameters, like the resuspension height and the pressure drop are far beyond the theoretical results. Evidently, a further increase of the Reynolds number indicates the transition to a less wavy interface. Finally, the linear stability analysis also predicts interfacial waves in the case of relatively small suspension heights. These results are in accordance with measurements for ripple-type instabilities as they occur under laminar and viscous conditions for a mono-layer of particles.
Nonlinear Kinetic Dynamics of Magnetized Weibel Instability
Palodhi, L; Pegoraro, F
2010-01-01
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Nonlinear spacial instability of a fluid sheet
Rangel, R. H.; Hess, C. F.
1990-01-01
The mechanism of nonlinear distortion of a fluid sheet leading to atomization is investigated numerically with the use of vortex dynamics and experimentally by means of holography. The configuration investigated consists of a planar fluid sheet emerging from a rectangular slit with and without coflowing air. The numerical model is two-dimensional, inviscid, and includes surface tension effects. The experimental results indicate the existence of well-defined three-dimensional structures. These are formed mainly by the nonlinear interaction of transverse and streamwise disturbances. The transverse disturbances are associated with the Kelvin-Helmholtz instability while the streamwise disturbances appear related to streamwise vortices possibly originating inside the nozzle.
Nonlinear spectroscopic studies of interfacial molecular ordering
Energy Technology Data Exchange (ETDEWEB)
Superfine, R.
1991-07-01
The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface. 32 refs., 4 figs., 2 tabs.
Limiting amplitudes of fully nonlinear interfacial tides and solitons
Aguiar-González, Borja; Gerkema, Theo
2016-08-01
A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi-Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.
Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study
Carvalho, Gabriel D.
2013-11-11
We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity. © 2013 American Physical Society.
Zhu, F. H.; Fu, Y. M.
2008-12-01
By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.
Interfacial instability in a time-periodic rotating Hele-Shaw Cell
Directory of Open Access Journals (Sweden)
Bouchgl J.
2014-01-01
Full Text Available The effect of time-periodic angular velocity on the interfacial instability of two immiscible, viscous fluids of different densities and confined in an annular Hele-Shaw cell is investigated. An inviscid linear stability analysis of the viscous and time dependent basic flow leads to a periodic Mathieu oscillator describing the evolution of the interfacial amplitude. We show that the relevant parameters that control the interface are the Bond number, viscosity ratio, Atwood number and the frequency number.
Deterministic aspects of nonlinear modulation instability
van Groesen, E; Karjanto, N
2011-01-01
Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurrence of extreme, rogue, waves. To that end a specific deterministic wavefield is investigated that develops extreme waves from a uniform background. For this explicitly described nonlinear extension of the Benjamin-Feir instability, the soliton on finite background of the NLS equation, the global down-stream evolving distortions, the time signal of the extreme waves, and the local evolution near the extreme position are investigated. As part of the search for conditions to obtain extreme waves, we show that the extreme wave has a specific optimization property for the physical energy, and comment on the possible validity for more realistic situations.
Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows
Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant
2015-01-01
We consider the genesis and dynamics of interfacial instability in gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of three main flow parameters (density contrast between liquid and gas, film thickness, pressure drop applied to drive the gas stream) on the interfacial dynamics. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable internal mode for low density contrast. The same linear stability approach provides a quantitative prediction for the onset of (partial) liquid flow reversal in terms of the gas and liquid flow rates. ...
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
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; Meer, van der R.M.; Lohse, D.; 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 shak
Effect of Horizontal Vibration on the Interfacial Instability in a Horizontal Hele-Shaw Cell
Directory of Open Access Journals (Sweden)
Souhar M.
2012-07-01
Full Text Available The effect of periodic oscillations on the interfacial instability of two immiscible fluids, confined in a horizontal Hele-Shaw cell, is investigated. A linear stability analysis of the basic state leads to a periodic Mathieu oscillator corresponding to the amplitude of the interface. Then, the threshold of parametric instability of the interface is characterized by harmonic or subharmonic periodic solutions. We show that the relevant parameters that control the interface are the Bond number, density ratio, Weber number and amplitude and frequency of oscillations.
Annual Progress Report. [Linear and nonlinear instability theory
Energy Technology Data Exchange (ETDEWEB)
Simon, A.; Catto, P.J.
1978-09-11
A number of topics in nonlinear and linear instability theory are covered in this report. The nonlinear saturation of the dissipative trapped electron instability is evaluated and its amplitude compares well with existing experimental observations. The nonlinear saturation of the drift cyclotron loss-cone mode is carried out for a variety of empty loss-cone distributions. The saturation amplitude is predicted to be small and stable. An improved linear theory of the collisionless drift instability in sheared magnetic fields yields the surprising result that no instability occurs for a wide range of parameters. Finally, the bump-on-tail calculation is shown to be unchanged by some recent results of Case and Siewart, and a rough time scale is established for the transition from the O'Neil trapping regime to the final time-asymptotic result.
Institute of Scientific and Technical Information of China (English)
F. H. Zhu; Y. M. Fu
2008-01-01
By considering the effect of interfacial damage and using the variation principle, three-dimensional nonli-near dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite dif-ference method, and the results are validated by compari-son with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.
Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows
Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant
2016-04-01
We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.
Nonlinear instability in simulations of Large Plasma Device turbulence
Friedman, B; Umansky, M V; Schaffner, D; Joseph, I
2013-01-01
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives $k_\\parallel = 0$ potential energy fluctuations, which then three-wave couple to $k_\\parallel \
Nonlinear vibration and rippling instability for embedded carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Soltani, Payam; Mehdipour, I. [Islamic Azad University, Semnan (Iran, Islamic Republic of); Farshidianfar, A. [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of); Ganji, D. D. [Babol University of Technology, Babol (Iran, Islamic Republic of)
2012-04-15
Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of single walled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.
Nonlinear Farley-Buneman instability with Dust Impurities.
Atamaniuk, B.; Volokitin, A. S.
2009-04-01
The regimes of nonlinear stabilization of instability of low frequency waves in magnetized, weakly ionized and inhomogeneous ionospheric dusty plasma are considered. In the lower ionosphere in the E--region, a complex process transforms wind energy into currents creating the E--region electrojet. If these currents exceed a certain critical amplitude, a streaming instability called the Farley--Buneman or a collisional two-stream instability develops. When the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. Then even system with finite number of interacting waves can realize a turbulent state in active media. At conditions when electrons are magnetized and characteristic time of density oscillations exceed the rate of electron ion collisions and electron dust collision the drift of electrons perpendicular to magnetic field is the main motion. Consequently, the main nonlinearity appears in result of convection of a density perturbation in one wave by another wave in the perpendicular to magnetic field and mathematically is expressed in a specific vector form The strong collisional damping of waves allow to assume that a typical perturbed state of plasma can be described as finite set of interacting waves. This allow to avoid difficulties of 3D simulations and to make full study of nonlinear stabilization and influence of the dust component in the conditions when the number of interacting waves keeps small by the strong competition of processes wave damping and instabilities Keywords: Dusty Plasmas, Farley-Buneman Instability, Nonlinear Stabilization. REFERENCES 1. M. Oppenheim and N. Otani, Geophysical Research Letters, 22, pp. 353-356, 1995. 2. A.V. Volosevich and C.V. Meister, Int. Journal of Geomagnetism and aeronomy, 3 pp.151-156, 2002 3. A. S. Volokitin and B. Atamaniuk, Reduced nonlinear description of Farley-Buneman instability
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Simulation of direct contact condensation of steam jets based on interfacial instability theories
Heinze, David; Schulenberg, Thomas; Class, Andreas; Behnke, Lars
2014-11-01
A simulation model for the direct contact condensation of steam in subcooled water is presented that allows to determine major parameters of the process such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin-Helmholtz and Rayleigh-Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations which is discretized by means of an explicit Runge-Kutta method. The simulation results are in good agreement with published experimental data over a wide range of pool temperatures and mass flow rates. funded by RWE Power AG.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
Nonlinear Evolution of the Ion-Ion Beam Instability
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.
1982-01-01
The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Liu, Yunqiao; Calvisi, Michael L.; Wang, Qianxi
2017-04-01
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents.
Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices
Li, Fei; Choudhari, Meelan M.; Duan, Lian; Chang, Chau-Lyan
2014-01-01
Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.
Directory of Open Access Journals (Sweden)
He-Ling Wang
2013-01-01
Full Text Available Magnetoelectric composite material is effective in transferring magnetic field into electric signal. In this paper, a nonlinear finite element method is present to model the magnetoelectric composite of ferroelectric and magnetostrictive material. In the method, the nonlinear and coupling behavior of magnetostrictive material such as Terfenol-D is considered. The nonuniform magnetic, electric, and mechanical field distributions are present. An interfacial transferring coefficient is defined to investigate the performance of interfacial mechanical coupling quantitatively, and the influence of the properties of interfacial bonding material and interfacial cracks on magnetoelectric coefficient is discussed. A new laminate ME composite of curved interface is proposed to overcome weak interfacial bonding.
Dey, Mohar; Bandyopadhyay, Dipankar; Sharma, Ashutosh; Qian, Shizhi; Joo, Sang Woo
2012-10-01
We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.
Modulational instability in fractional nonlinear Schrödinger equation
Zhang, Lifu; He, Zenghui; Conti, Claudio; Wang, Zhiteng; Hu, Yonghua; Lei, Dajun; Li, Ying; Fan, Dianyuan
2017-07-01
Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the MI gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and MI bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.
Nonlinear effects at the Fermilab Recycler e-cloud instability
Balbekov, V
2016-01-01
Theoretical analysis of e-cloud instability in the Fermilab Recycler is represented in the paper. The e-cloud in strong magnetic field is treated as a set of immovable snakes each being initiated by some proton bunch. It is shown that the instability arises because of injection errors of the bunches which increase in time and from the batch to its bunch being amplified by the e-cloud electric field. The particular attention is given to nonlinear additions to the cloud field. It is shown that the nonlinearity is the main factor which restricts growth of the bunch amplitude. Possible role of the field free parts of the Recycler id discussed as well. Results of calculations are compared with experimental data demonstrating good correlation.
Nonlinear Effects at the Fermilab Recycler e-Cloud Instability
Energy Technology Data Exchange (ETDEWEB)
Balbekov, V. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2016-06-10
Theoretical analysis of e-cloud instability in the Fermilab Recycler is represented in the paper. The e-cloud in strong magnetic field is treated as a set of immovable snakes each being initiated by some proton bunch. It is shown that the instability arises because of injection errors of the bunches which increase in time and from bunch to bunch along the batch being amplified by the e-cloud electric field. The particular attention is given to nonlinear additions to the cloud field. It is shown that the nonlinearity is the main factor which restricts growth of the bunch amplitude. Possible role of the field free parts of the Recycler id discussed as well. Results of calculations are compared with experimental data demonstrating good correlation.
Sun, Yuxiang; Mei, Ling; Han, Ning; Ding, Xinyi; Yu, Caihao; Yang, Wenjuan; Ruan, Gang
2017-06-01
The interfacial instability process is an emerging general method to fabricate nanocrystal-encapsulated micelles (also called micellar nanocrystals) for biological detection, imaging, and therapy. The present work utilized fluorescent semiconductor nanocrystals (quantum dots or QDs) as the model nanocrystals to investigate the interfacial instability-based fabrication process of nanocrystal-encapsulated micelles. Our experimental results suggest intricate and intertwined roles of the emulsion droplet size and the surfactant poly (vinyl alcohol) (PVA) used in the fabrication process of QD-encapsulated poly (styrene-b-ethylene glycol) (PS-PEG) micelles. When no PVA is used, no emulsion droplet and thus no micelle is successfully formed; Emulsion droplets with large sizes ( 25 μm) result in two types of QD-encapsulated micelles, one of which is colloidally stable QD-encapsulated PS-PEG micelles while the other of which is colloidally unstable QD-encapsulated PVA micelles; In contrast, emulsion droplets with small sizes ( 3 μm or smaller) result in only colloidally stable QD-encapsulated PS-PEG micelles. The results obtained in this work not only help to optimize the quality of nanocrystal-encapsulated micelles prepared by the interfacial instability method for biological applications but also offer helpful new knowledge on the interfacial instability process in particular and self-assembly in general.
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.
Nonlinear interplay of Alfven instabilities and energetic particles in tokamaks
Biancalani, A; Cole, M; Di Troia, C; Lauber, Ph; Mishchenko, A; Scott, B; Zonca, F
2016-01-01
The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of the frequency, growth rate and radial structure of the TAE, depending on the evolution of the EP distribution in phase space. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. This nonlinear evolution is found to be correctly reproduced by means of a quasilinear model, namely a model where the linear effects of the nonlinearly modified EP distri...
ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis
Eberhart, C. J.; Casiano, M. J.
2015-01-01
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
Miles, Aaron
2004-11-01
In this talk we discuss the nature of late-time, broad-banded instability development at an interface when a strong blast wave travels from a heavier to lighter fluid, as is the case in a supernova explosion. After a short period of Richtmyer-Meshkov growth, the interface is unstable via the Rayleigh-Taylor mechanism, which rapidly becomes the dominant energy source for growth. This situation is distinct from the classical case in two important ways, both of which can be understood in terms of a bubble merger model we have developed for blast-wave-driven systems. Rather than the constant acceleration feeding the instability to spawn ever larger scales and accelerate the growth, the decaying acceleration in the blast-wave case leads to a decay in the RT growth rate, and a freezing in of a preferred largest scale, which is dependent on the precise details of the system. In the language of bubble-merger models, this can be understood in terms of the time for the generation of the next largest scale being longer than the lifetime of the blast wave. Secondly, the continual expansion behind the blast front precludes the emergence of a self-similar regime, independent of the initial conditions, in the planar case. Self-similarity may be recovered in diverging systems but may be difficult to observe in reality because of rather restrictive conditions that must be met. These observations are borne out by hi-resolution numerical simulations using the higher order Godunov AMR hydrocode Raptor in 2 and 3D, and explain other simulations of instability growth in supernovae explosions; the initial "interfacial" structure is likely very important in determining the late-time growth. The model predictions are also consistent with numerous images of natural and manmade explosions.
Nonlinear evolution and final fate of (charged) superradiant instability
Bosch, Pablo; Lehner, Luis
2016-01-01
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner--Nordstr\\"om-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Optimal frequency conversion in the nonlinear stage of modulation instability
Bendahmane, A; Kudlinski, A; Szriftgiser, P; Conforti, M; Wabnitz, S; Trillo, S
2015-01-01
We investigate multi-wave mixing associated with the strongly pump depleted regime of induced modulation instability (MI) in optical fibers. For a complete transfer of pump power into the sideband modes, we theoretically and experimentally demonstrate that it is necessary to use a much lower seeding modulation frequency than the peak MI gain value. Our analysis shows that a record 95 % of the input pump power is frequency converted into the comb of sidebands, in good quantitative agreement with analytical predictions based on the simplest exact breather solution of the nonlinear Schr\\"odinger equation.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生
2001-01-01
By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.
Bhowmick, Aklant K.; Abarzhi, Snezhana
2016-11-01
Rayleigh Taylor instability in a power-law time dependent acceleration field is investigated theoretically for a flow with the symmetry group p6mm (hexagon) in the plane normal to acceleration. In the nonlinear regime, regular asymptotic solutions form a one-parameter family. The physically significant solution is identified with the one having the fastest growth and being stable (bubble tip velocity). Two distinct regimes are identified depending on the acceleration exponent. Particularly, the RM-type regime, where the dynamics is identical to conventional RM instability and is dominated by initial conditions, and the RT-type regime where the dynamics is dominated by the acceleration term. For the latter, the time dependence has profound effects on the dynamics. In the RT non-linear regime, the time dependence has no consequence on the morphology of the bubbles; the growth rate (bubble tip velocity) evolves as power law with the exponent set by the acceleration. The solutions for a one-parameter family, and are convergent with exponential decay of Fourier amplitudes. The solutions are stable at maximum tip velocity, whereas flat bubbles are unstable, and the growth/decay of perturbations is no longer purely exponential and depends on the acceleration exponent. The work is supported by the US National Science Foundation.
Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings
DEFF Research Database (Denmark)
Corney, Joel F.; Bang, Ole
2004-01-01
We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....
Nonlinear evolution of drift instabilities in the presence of collisions
Energy Technology Data Exchange (ETDEWEB)
Federici, J.F.; Lee, W.W.; Tang, W.M.
1986-07-01
Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with ephi/T/sub e/ approx. = (..omega../sub l//..cap omega../sub i/)/(k/sub perpendicular/rho/sub s/)/sup 2/. The associated quasilinear diffusion, which increases with collisionality, takes the form of D/sub ql/ approx. = ..gamma../sub l//k/sub perpendicular//sup 2/, where ..omega../sub l/ and ..gamma../sub l/ are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it remains finite even in the collisionless limit.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Reyna, Albert S
2014-01-01
We present a procedure for nonlinearity management of metal-dielectric composites. Varying the volume fraction occupied by silver nanoparticles suspended in acetone we could cancel the refractive index related to the third-order susceptibility, $\\chi_{eff}^{(3)}$, and the nonlinear refraction behavior was due to the fifth-order susceptibility, $\\chi_{eff}^{(5)}$. Hence, in a cross-phase modulation experiment, we demonstrated for the first time the effect of spatial-modulation- instability due to $\\chi_{eff}^{(5)}$. The results are corroborated with numerical calculations based on a generalized Maxwell-Garnet model.
Helton, Kristen L; Yager, Paul
2007-11-01
As part of a project to develop an integrated microfluidic biosensor for the detection of small molecules in saliva, practical issues of extraction of analytes from non-Newtonian samples using an H-filter were explored. The H-filter can be used to rapidly and efficiently extract small molecules from a complex sample into a simpler buffer. The location of the interface between the sample and buffer streams is a critical parameter in the function of the H-filter, so fluorescence microscopy was employed to monitor the interface position; this revealed apparently anomalous fluorophore diffusion from the samples into the buffer solutions. Using confocal microscopy to understand the three-dimensional distribution of the fluorophore, it was found that the interface between the non-Newtonian sample and Newtonian buffer was both curved and unstable. The core of the non-Newtonian sample extended into the Newtonian buffer and its position was unstable, producing a fluorescence intensity profile that gave rise to the apparently anomalously fast fluorophore transport. These instabilities resulted from the pairing of rheologically dissimilar fluid streams and were flowrate dependent. We conclude that use of non-Newtonian fluids, such as saliva, in the H-filter necessitates pretreatment to reduce viscoelasticity. The interfacial variation in position, stability and shape caused by the non-Newtonian samples has substantial implications for the use of biological samples for quantitative analysis and analyte extraction in concurrent flow extraction devices.
Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis
Merchant, G. J.; Braun, R. J.; Brattkus, K.; Davis, S. H.
1992-01-01
In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.
Bhowmick, Aklant K.; Abarzhi, Snezhana
2016-10-01
Rayleigh Taylor instability in a power-law time dependent acceleration field is investigated for a flow with the symmetry group p6mm (hexagonal) in the plane normal to acceleration. The Regular asymptotic solutions form a one-parameter family and the physically significant solution is identified with the one having the fastest growth and being stable (bubble tip velocity). Two distinct regimes are identified dependent on the acceleration exponent, the RM-type regime, where the dynamics is identical to conventional RM instability and is dominated by initial conditions, and the RT-type regime where the dynamics is dominated by the acceleration term. For the latter, the time dependence has profound effects on the dynamics. In the RT non-linear regime, the time dependence has no consequence on the morphology of the bubbles but the growth rate (bubble tip velocity) evolves as power law with the exponent set by the acceleration. The solutions for a one-parameter family, and are convergent with exponential decay of Fourier amplitudes close to the physical solution. The solutions are stable at maximum tip velocity and flat bubbles are unstable, and the growth/decay of perturbations is no longer purely exponential and depends on the acceleration exponent. The work is supported by the US National Science Foundation.
Khanwale, Makrand A.; Khadamkar, Hrushikesh P.; Mathpati, Channamallikarjun S.
2015-11-01
Physics of development of flow structures around the drop rising with solute transfer is highly influenced by the interfacial behaviour and is remarkably different than a particle rising under the same conditions. We report on the use of simultaneous particle image velocimetry-planar laser induced fluorescence technique to measure scalar and velocity fields around a drop rising in a quiescent liquid channel. The selected continuous phase is glycerol, and the drop consists of a mixture of toluene, acetone, and a dye rhodamine-6G, with acetone working as a interfacial tension depressant. The drop lies in the spherical region with Eötvös number, Eo = 1.95, Morton number, M = 78.20 and the particle Reynolds number being, Rep = 0.053. With Rep approaching that of creeping flow, we analyse the effect of interfacial instabilities solely, contrary to other investigations [M. Wegener et al., "Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets," Int. J. Heat Mass Transfer 52, 2543-2551 (2009); S. Burghoff and E. Y. Kenig, "A CFD model for mass transfer and interfacial phenomena on single droplets," AIChE J. 52, 4071-4078 (2006); J. Wang et al., "Numerical simulation of the Marangoni effect on transient mass transfer from single moving deformable drops," AIChE J. 57, 2670-2683 (2011); R. F. Engberg, M. Wegener, and E. Y. Kenig, "The impact of Marangoni convection on fluid dynamics and mass transfer at deformable single rising droplets—A numerical study," Chem. Eng. Sci. 116, 208-222 (2014)] which account for turbulence as well as interfacial instabilities with Rep in the turbulent range. The velocity and concentration fields obtained are subjected to scale-wise energy decomposition using continuous wavelet transform. Scale-wise probability distribution functions of wavelet coefficients are calculated to check intermittent non-Gaussian behaviour for simultaneous velocity and scalar statistics. Multi-fractal singularity spectra for scalar
Nonlinear Weibel Instability and Turbulence in Strong Collisionless Shocks
Energy Technology Data Exchange (ETDEWEB)
Medvedev, Mikhail M.
2008-08-31
This research project was devoted to studies of collisionless shocks, their properties, microphysics and plasma physics of underlying phenomena, such as Weibel instability and generation of small-scale fields at shocks, particle acceleration and transport in the generated random fields, radiation mechanisms from these fields in application to astrophysical phenomena and laboratory experiments (e.g., laser-plasma and beam-plasma interactions, the fast ignition and inertial confinement, etc.). Thus, this study is highly relevant to astrophysical sciences, the inertial confinement program and, in particular, the Fast Ignition concept, etc. It makes valuable contributions to the shock physics, nonlinear plasma theory, as well as to the basic plasma science, in general.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Directory of Open Access Journals (Sweden)
Liu Chang-Jiang
2011-01-01
Full Text Available This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM with spline function method (SFM to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.
Nonlinear Saturation Amplitude in Classical Planar Richtmyer-Meshkov Instability
Liu, Wan-Hai; Wang, Xiang; Jiang, Hong-Bin; Ma, Wen-Fang
2016-04-01
The classical planar Richtmyer-Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh-Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI. Supported by the National Natural Science Foundation of China under Grant Nos. 11472278 and 11372330, the Scientific Research Foundation of Education Department of Sichuan Province under Grant No. 15ZA0296, the Scientific Research Foundation of Mianyang Normal University under Grant Nos. QD2014A009 and 2014A02, and the National High-Tech ICF Committee
Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures
Institute of Scientific and Technical Information of China (English)
彭妙娟; 程玉民
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
The dynamics of rapid fracture: instabilities, nonlinearities and length scales.
Bouchbinder, Eran; Goldman, Tamar; Fineberg, Jay
2014-04-01
The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the almost singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, namely linear elastic fracture mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined 'weakly nonlinear fracture mechanics', where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, ℓnl. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of ℓnl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wavelength is determined by ℓnl. We conclude by delineating outstanding challenges in the field.
NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION
Institute of Scientific and Technical Information of China (English)
Yiming Fu; Rengui Bi; Pu Zhang
2009-01-01
A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waais forces as well as the non-coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube (DWNT) can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.
Rosin, M S; Rincon, F; Cowley, S C
2010-01-01
Plasmas have a natural tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius with growth rates of a fraction of the ion cyclotron frequency - much faster than either the global dynamics or local turbulence. The instabilities can dramatically modify the macroscopic dynamics of the plasma. Nonlinear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta. This nonlinear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel firehose instability in a high-beta plasma. A closed nonlinear equation for the firehose turbulence is derived and solved. In the nonlinear regime, the instability leads to secular (~t) growth of magnetic fluctuations. The fluctuations develop a k^{-3} spectrum, extending from scales somewhat larger than r...
Directory of Open Access Journals (Sweden)
Singh M.
2016-02-01
Full Text Available The instability of the plane interface between two uniform, superposed and streaming Rivlin-Ericksen elastico-viscous fluids through porous media, including the ‘effective interfacial tension’ effect, is considered. In the absence of the ‘effective interfacial tension’ stability/instability of the system as well as perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbation in all other directions, there exists instability for a certain wave number range. The ‘effective interfacial tension’ is able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2002-01-01
Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.
Bentley, Sean J; Heebner, John E; Boyd, Robert W
2006-04-01
We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Instability due to interfacial tension in parallel liquid-liquid flow
Rodriguez, Oscar M. H.
2016-06-01
The frequent occurrence of multiphase flows in pipes has motivated a great research interest over the last decades. The particular case of liquid-liquid flow is commonly encountered in the petroleum industry, where a number of applications involve oil-water flow such as crude oil production in directional wells. However, it has not received the same attention when compared to gas-liquid flow. In addition, most of the available information has to do with flow in pipes. When it comes to flows in annular ducts the data are scanty. A general transition criterion has been recently proposed in order to obtain the stratified and core-annular flow-pattern transition boundaries in viscous oil-water flow. The proposed criterion was based on an one-dimensional two-fluid model of liquid-liquid two-phase flow. A stability analysis was carried out and interfacial tension is considered. A new destabilizing term arises, which is a function of the cross-section curvature of the interface. It is well accepted that interfacial tension favors the stable condition. However, the analysis of the new interfacial-tension term shows that it can actually destabilize the basic flow pattern, playing an important role in regions of extreme volumetric fractions. Such an interesting effect seems to be more pronounced in flows of viscous fluids and in annular-duct flow. The effect of interfacial tension is explored and the advantages of using a more complete model are discussed and illustrated through comparisons with experimental data from the literature. The evaluation of the effects of fluid viscosity and interfacial tension allows the correction and enhancement of transition models based essentially on data of pipe flow of low viscosity fluids.
Chaves Filho, V. L.; Lima, R. P. A.; Lyra, M. L.
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
Demekhin, E A; Polyanskikh, S V
2011-01-01
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number sele...
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Liu Chang-Jiang; Zheng Zhou-Lian; Huang Cong-Bing; He Xiao-Ting; Sun Jun-Yi; Chen Shan-Lin
2011-01-01
This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular l...
A Weakly Nonlinear Model for Kelvin-Helmholtz Instability in Incompressible Fluids
Institute of Scientific and Technical Information of China (English)
WANG Li-Feng; YE Wen-Hua; FAN Zheng-Feng; XUE Chuang; LI Ying-Jun
2009-01-01
A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.
Nonlinear evolution of mirror instability in the Earth's magnetosheath in pic simulations
Ahmadi, Narges
Mirror modes are large amplitude non-propagating structures frequently observed in the magnetosheath and they are generated in space plasma environments with proton temperature anisotropy of larger than one. The proton temperature anisotropy also drives the proton cyclotron instability which has larger linear growth rate than that of the mirror instability. Linear dispersion theory predicts that electron temperature anisotropy can enhance the mirror instability growth rate while leaving the proton cyclotron instability largely unaffected. Contrary to the hypothesis, electron temperature anisotropy leads to excitement of the electron whistler instability. Our results show that the electron whistler instability grows much faster than the mirror instability and quickly consumes the electron free energy, so that there is not enough electron temperature anisotropy left to significantly impact the evolution of the mirror instability. Observational studies have shown that the shape of mirror structures is related to local plasma parameters and distance to the mirror instability threshold. Mirror structures in the form of magnetic holes are observed when plasma is mirror stable or marginally mirror unstable and magnetic peaks are observed when plasma is mirror unstable. Mirror structures are created downstream of the quasi-perpendicular bow shock and they are convected toward the magnetopause. In the middle magnetosheath, where plasma is mirror unstable, mirror structures are dominated by magnetic peaks. Close to the magnetopause, plasma expansion makes the region mirror stable and magnetic peaks evolve to magnetic holes. We investigate the nonlinear evolution of mirror instability using expanding box Particle-in-Cell simulations. We change the plasma conditions by artificially enlarging the simulation box over time to make the plasma mirror stable and investigate the final nonlinear state of the mirror structures. We show that the direct nonlinear evolution of the mirror
Xu, Jian-Jun
1989-01-01
The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.
The Influence of Dust on the Farley-Buneman instability. Nonlinear regimes.
Atamaniuk, Barbara
In the lower ionosphere in the E-region, a complex process transforms wind energy into currents creating the E-region electrojet. If these currents exceed a certain critical amplitude, a streaming instability called the Farley-Buneman or a collisional two-stream instability develops. This instability grows more rapidly at shorter wavelengths and the waves propagate nearly perpendicular to the magnetic field. It is well known that even system with finite number of interacting waves can realize a turbulent state in active media. In such cases, when the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. The perturbed ionospheric plasma is one of important example of such active media. The regimes of nonlinear stabilization of instability of low frequency waves in magnetized, weakly ionized and inhomogeneous ionospheric dusty plasma are considered. We make assumptions that the Earth magnetic field has no influence on the ions and on the dust particles so only the electrons are magnetized. If characteristic time of plasma density oscillations exceeds an electron collision frequency the basic is drift motion of electrons and, accordingly, the vector nonlinearity is the strongest. We study of nonlinear stabilization and influence of the dust component, conditions of stochasticity and the different regimes in the conditions when the number of interacting waves keeps small by the strong competition of processes wave damping and instabilities are considered. *This research is supported by KBN grant 0TOOA 01429 1. Meers Oppenheim and Niels Otani, Hybrid Simulations of the Saturated Farley-Buneman Instability in the Ionosphere, Geophysical Research Letters, 22, pp. 353-356, 1995 2. Meers Oppenheim and Niels Otani and Corrado Ronchi, Saturation of the Farley-Buneman instability via nonlinear electron ExB drifts, Journal of Geophysical Research, 101
Vécsei, Miklós; Hardt, Steffen
2016-01-01
The stability of liquid films coating the walls of a parallel-plate channel and sheared by a pressure-driven gas flow along the channel centre is studied. The films are susceptible to a long-wavelength instability, whose dynamic behaviour is found - for sufficiently low Reynolds numbers and thick gas layers - to be described by two coupled non-linear partial differential equations. To the best of our knowledge, such coupled fully non-linear equations for the film thicknesses have not been derived previously. A linear stability analysis conducted under the condition that the material properties and the initial undisturbed liquid film thicknesses are equal can be utilized to determine whether the interfaces are predominantly destabilized by the variations of the shear stress or by the pressure gradient acting upon them. The analysis of the weakly non-linear equations performed for this case shows that instabilities corresponding to a vanishing Reynolds number are absent from the system. Moreover, for this confi...
Nonlinear electron-magnetohydrodynamic simulations of three dimensional current shear instability
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj [Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau (Germany); Das, Amita; Sengupta, Sudip; Kaw, Predhiman [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-09-15
This paper deals with detailed nonlinear electron-magnetohydrodynamic simulations of a three dimensional current shear driven instability in slab geometry. The simulations show the development of the instability in the current shear layer in the linear regime leading to the generation of electromagnetic turbulence in the nonlinear regime. The electromagnetic turbulence is first generated in the unstable shear layer and then spreads into the stable regions. The turbulence spectrum shows a new kind of anisotropy in which power transfer towards shorter scales occurs preferentially in the direction perpendicular to the electron flow. Results of the present three dimensional simulations of the current shear instability are compared with those of our earlier two dimensional simulations of sausage instability. It is found that the flattening of the mean velocity profile and thus reduction in the electron current due to generation of electromagnetic turbulence in the three dimensional case is more effective as compared to that in the two dimensional case.
Chin, Siu A
2007-01-01
Since the kinetic and the potential energy term of the real time nonlinear Schr\\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\\dt k_{max}^2{<\\atop\\sim}2 \\pi$, where $k_{max}=\\pi/\\Delta x$.
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
Nonlinear evolution of the modulational instability under weak forcing and damping
Directory of Open Access Journals (Sweden)
J. Touboul
2010-12-01
Full Text Available The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a and Wu et al. (2006. Their results were extended theoretically by Kharif et al. (2010 who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010 from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.
Energy Technology Data Exchange (ETDEWEB)
Eliasson, B., E-mail: bengt.eliasson@strath.ac.uk [SUPA, Physics Department, John Anderson Building, Strathclyde University, Glasgow G4 0NG, Scotland (United Kingdom); Lazar, M., E-mail: mlazar@tp4.rub.de [Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum (Germany)
2015-06-15
This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.
Novick-Cohen, A.
1987-05-01
Directional solidification processes in the presence of an impurity are studied in the limit in which the dimensionless parameter overlineW = {GD}/{VC}0( g + ⨍ c) is small. Here G is the imposed temperature gradient, D is the diffusion coefficient of the impurity, V is the imposed transport velocity, g is equal to minus the slope of the liquidus line, C0 is the impurity concentration at the liquid side of a planar interface, and ⨍ c is a coefficient reflecting deviations from local thermal equilibrium. The dynamics of interfacial kinetics becomes important in this limit and the phenomenological model of Coriell and Sekerka [J. Cryst. Growth 61 (1983) 499-508] is used to model these processes. In this limit, the Kuramoto-Sivashinsky equation is shown to be an asymptotically valid description of the interfacial dynamics. The Kuramoto-Sivashinsky equation is known to exhibit intermittancy superimposed on a relatively stable array of cusps or wrinkles [Michelson and Sivashinsky, Acta Astronautica 4 (1977) 1207-1221] and thus may give a reasonable limiting description of the solidification interface just before coherency is lost. These cusps may also be important in the initiation of dendritic growth by serving as defect points [Schaefer and Glicksman, Met. Trans. 1 (1970) 1973-1978].
Directory of Open Access Journals (Sweden)
Ghader Rezazadeh
2007-07-01
Full Text Available In this paper, the effect of residual stress on divergence instability of a rectangular microplate subjected to a nonlinear electrostatic pressure for different geometrical properties has been presented. After deriving the governing equation and using of Step-by-Step Linearization Method (SSLM, the governing nonlinear equation has been linearized. By applying the finite difference method (FDM to a rectangular mesh, the linearized equation has been discretized. The results show, residual stresses have considerable effects on Pull-in phenomena. Tensile residual stresses increase pull-in voltage and compressive decrease it. The effect of different geometrical properties on divergence instability has also been studied.
Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer
Sarkar, Niladri; Basu, Abhik
2015-11-01
We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient Γ . Being controlled by Γ , our model provides a unified framework to describe the long-wavelength behavior of a variety of thin polar-ordered systems, ranging from wet to dry active matter and free-standing active films. Investigations of the linear instabilities around a chosen orientationally ordered uniform reference state reveal generic moving and static instabilities in the system that can depend sensitively on Γ . Based on our results, we discuss estimation of bounds on Γ in experimentally accessible systems.
Nonlinear instabilities induced by the F coil power amplifier at FTU: Modeling and control
Energy Technology Data Exchange (ETDEWEB)
Zaccarian, L. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Boncagni, L. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Cascone, D. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Centioli, C. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Cerino, S. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Gravanti, F.; Iannone, F. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Mecocci, F.; Pangione, L. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Podda, S. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Vitale, V. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy)], E-mail: vitale@frascati.enea.it; Vitelli, R. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy)
2009-06-15
In this paper we focus on the instabilities caused by the nonlinear behavior of the F coil current amplifier at FTU. This behavior induces closed-loop instability of the horizontal position stabilizing loop whenever the requested current is below the circulating current level. In the paper we first illustrate a modeling phase where nonlinear dynamics are derived and identified to reproduce the open-loop responses measured by the F coil current amplifier. The derived model is shown to successfully reproduce the experimental behavior by direct comparison with experimental data. Based on this dynamic model, we then reproduce the closed-loop scenario of the experiment and show that the proposed nonlinear model successfully reproduces the nonlinear instabilities experienced in the experimental sessions. Given the simulation setup, we next propose a nonlinear control solution to this instability problem. The proposed solution is shown to recover stability in closed-loop simulations. Experimental tests are scheduled for the next experimental campaign after the FTU restart.
Massive gravity: nonlinear instability of the homogeneous and isotropic universe
De Felice, Antonio; Mukohyama, Shinji
2012-01-01
We study the propagating modes for nonlinear massive gravity on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. Since this ghost mode can be considered as a leading nonlinear perturbation around a homogeneous and isotropic background, we conclude that the universe in this theory must be either inhomogeneous or anisotropic.
AN INSTABILITY THEOREM FOR A KIND OF SEVENTH ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
This paper considers a kind of seventh order nonlinear differential equations with a deviating argument.By means of the Lyapunov direct method,some sufficient conditions are established to show the instability of the zero solution to the equation.Our result is new and complements the corresponding result of [5].
Effect of four-dimensional variational data assimilation in case of nonlinear instability
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The effect of four-dimensional variational data assimilation on the reduction of the forecast errors is investigated for both stable and unstable flows. Numerical results show that the effect is generally positive. Particularly,its effect is much more significant in the presence of nonlinear instability
Passamonti, A
2011-01-01
We study the damping of the gravitational radiation-driven f-mode instability in ro- tating neutron stars by nonlinear bulk viscosity in the so-called supra-thermal regime. In this regime the dissipative action of bulk viscosity is known to be enhanced as a result of nonlinear contributions with respect to the oscillation amplitude. Our anal- ysis of the f-mode instability is based on a time-domain code that evolves linear perturbations of rapidly rotating polytropic neutron star models. The extracted mode frequency and eigenfunctions are subsequently used in standard energy integrals for the gravitational wave growth and viscous damping. We find that nonlinear bulk vis- cosity has a moderate impact on the size of the f-mode instability window, becoming an important factor and saturating the mode's growth at a relatively large oscillation amplitude. We show that a similar result holds for the damping of the inertial r-mode instability by nonlinear bulk viscosity. In addition, we show that the action of bulk v...
The nonlinear saturation of the non-resonant kinetically driven streaming instability
Gargate, L; Niemiec, J; Pohl, M; Bingham, R; Silva, L O
2010-01-01
A non-resonant instability for the amplification of the interstellar magnetic field in young Supernova Remnant (SNR) shocks was predicted by Bell (2004), and is thought to be relevant for the acceleration of cosmic ray (CR) particles. For this instability, the CRs streaming ahead of SNR shock fronts drive electromagnetic waves with wavelengths much shorter than the typical CR Larmor radius, by inducing a current parallel to the background magnetic field. We explore the nonlinear regime of the non-resonant mode using Particle-in-Cell (PIC) hybrid simulations, with kinetic ions and fluid electrons, and analyze the saturation mechanism for realistic CR and background plasma parameters. In the linear regime, the observed growth rates and wavelengths match the theoretical predictions; the nonlinear stage of the instability shows a strong reaction of both the background plasma and the CR particles, with the saturation level of the magnetic field varying with the CR parameters. The simulations with CR-to-background ...
EFFECT OF HEAT EXCHANGE ON THE INTERFACIAL INSTABILITY OF GAS-LIQUID JET
Institute of Scientific and Technical Information of China (English)
王志亮; 周哲玮
2003-01-01
The classical linear instability theory was applied to the planar stratified two-layers flow with high speed compressible gas layer impacting on incompressible viscous liquidlayer. The walls were kept at different temperatures, resulting in heat transfer across thelayers. The thermal conductivity and the density of the gas were alerted when thetemperature changes. After some treatment, a four-order stiff ordinary differential equationwas derived, and numerical integration and multi-shooting method were used to solve thisequation for its spatial mode calculation. The numerical results of characteristic parametersshow good coincidence with other models. At the same time, when the wall temperatureratio decreases, as well as the Reynolds number and the gas thermal conductivity changeincreases, the atomization would be more efficient and producing finer droplets. And theresults show good fit with the experimental datum of HJE. Co. Inc ( Glens Falls, NY,USA ).
AdS nonlinear instability: moving beyond spherical symmetry
Dias, Oscar J C
2016-01-01
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.
Nonlinear effects of energetic particle driven instabilities in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Bruedgam, Michael
2010-03-25
In a tokamak plasma, a population of superthermal particles generated by heating methods can lead to a destabilization of various MHD modes. Due to nonlinear wave-particle interactions, a consequential fast particle redistribution reduces the plasma heating and can cause severe damages to the wall of the fusion device. In order to describe the wave-particle interaction, the drift-kinetic perturbative HAGIS code is applied which evolves the particle trajectories and the waves nonlinearly. For a simulation speed-up, the 6-d particle phase-space is reduced by the guiding centre approach to a 5-d description. The eigenfunction of the wave is assumed to be invariant, but its amplitude and phase is altered in time. A sophisticated {delta}/f-method is employed to model the change in the fast particle distribution so that numerical noise and the excessive number of simulated Monte-Carlo points are reduced significantly. The original code can only calculate the particle redistribution inside the plasma region. Therefore, a code extension has been developed during this thesis which enlarges the simulation region up to the vessel wall. By means of numerical simulations, this thesis addresses the problem of nonlinear waveparticle interactions in the presence of multiple MHD modes with significantly different eigenfrequencies and the corresponding fast particle transport inside the plasma. In this context, a new coupling mechanism between resonant particles and waves has been identified that leads to enhanced mode amplitudes and fast particle losses. The extension of the code provides for the first time the possibility of a quantitative and qualitative comparison between simulation results and recent measurements in the experiment. The findings of the comparison serve as a validation of both the theoretical model and the interpretation of the experimental results. Thus, a powerful interface tool has been developed for a deeper insight of nonlinear wave-particle interaction
Non-linear Study of Bell's Cosmic Ray Current-driven Instability
Riquelme, Mario A
2008-01-01
The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004), consists of non-resonant, growing plasma waves driven by the electric current of cosmic rays (CRs) that stream along the magnetic field ahead of both relativistic and non-relativistic shocks. Combining an analytic, kinetic model with one-, two-, and three-dimensional particle-in-cell simulations, we confirm the existence of this instability in the kinetic regime and determine its saturation mechanisms. In the linear regime, we show that, if the background plasma is well magnetized, the CRCD waves grow exponentially at the rates and wavelengths predicted by the analytic dispersion relation. The magnetization condition implies that the growth rate of the instability is much smaller than the ion cyclotron frequency. As the instability becomes non-linear, significant turbulence forms in the plasma. This turbulence reduces the growth rate of the field and damps the shortest wavelength modes, making the dominant wavelength, \\lambda_d, grow ...
The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities
Chang, Philip; Lamberts, Astrid
2014-01-01
Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to ap...
Barker, Adrian J
2016-01-01
I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the nonlinear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin-orbit alignment on a similar timescale as the spin synchronisation. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability,...
Yano, T.; Nishino, K.; Ueno, I.; Matsumoto, S.; Kamotani, Y.
2017-04-01
This paper reports the sensitivity of hydrothermal wave (HTW) instability of Marangoni convection to the interfacial heat transfer in liquid bridges (LBs) of high Prandtl number fluids (Pr = 67, 112, and 207) formed under the microgravity environment on the International Space Station. The data for instability are collected for a wide range of AR and for TC = 15 and 20 °C, where AR is the aspect ratio (=height/diameter) of the LB and TC is the cooled disk temperature. A significant decrease in critical oscillation frequency as well as an appreciable decrease in the critical Marangoni number is observed for AR > 1.25. This drastic change of instability mechanisms is associated with the reversal of axial traveling direction of HTWs and roll-structures as reported previously. It is found that this reversal is closely related to the interfacial heat transfer, which is evaluated numerically through accounting for both convective and radiative components. A heat transfer ratio, QI/QH, is introduced as a dimensionless parameter for interfacial heat transfer, where QI and QH are the heat transfer rates at the LB-gas and LB-heated disk interfaces, respectively. It is found that HTWs travel in the same direction as the surface flow for QI/QH > 0 (heat-loss condition) while in the opposite direction for QI/QH alters slightly but appreciably the basic temperature and flow field, the alteration that is not accounted for in the previous linear stability analyses for an infinite LB.
AdS nonlinear instability: moving beyond spherical symmetry
Dias, Óscar J. C.; Santos, Jorge E.
2016-12-01
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation (Dafermos and Holzegel 2006 Seminar at DAMTP (University of Cambridge) available at https://dpmms.cam.ac.uk/~md384/ADSinstability.pdf, Bizon and Rostworowski 2011 Phys. Rev. Lett. 107 031102). We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied by Bizon and Rostworowski. In contrast with Bizon and Rostworowski, we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied by Bizon and Rostworowski. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of Bizon and Rostworowski. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.
Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
Hendi, S H; Panah, B Eslam; Momennia, M
2015-01-01
Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in the context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that although there is not physical small black hole, large black holes are physical and enjoy thermal stability in gravity's rainbow.
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation.
A nonlinear dynamical system for combustion instability in a pulse model combustor
Takagi, Kazushi; Gotoda, Hiroshi
2016-11-01
We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.
Palodhi, L; Pegoraro, F; 10.1088/0741-3335/51/12/125006
2010-01-01
The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional velocity space. It is found that the electromagnetic fields generated by this instability cause a strong deformation of the electron distribution function in phase space, corresponding to highly filamented magnetic vortices. Eventually, these deformations lead to the generation of short wavelength Langmuir modes that form highly localized electrostatic structures corresponding to jumps of the electrostatic potential.
Simulations and model of the nonlinear Richtmyer-Meshkov instability (U)
Energy Technology Data Exchange (ETDEWEB)
Dimonte, Guy [Los Alamos National Laboratory
2009-01-01
The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (20). The purpose of the simulations is to develop a nonlinear model of the RM instability that is accurate to the regime of inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and initial amplitude kh{sub o} (k {triple_bond} wavenumber) of the perturbation. The FLASH code is first validated by obtaining excellent agreement with RM experiments well into the nonlinear regime. The results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A and kh{sub o} but not for the values characteristic of ICF and ejecta formation. As a result, a new nonlinear model is developed that captures the simulation results consistent with potential flow and for a broader range of A and kh{sub o}.
Active control and nonlinear feedback instabilities in the earth's radiation belts
Silevitch, M. B.; Villalon, E.; Rothwell, P. L.
The stability of trapped particle fluxes are examined near the Kennel-Petschek limit. In the absence of coupling between the ionosphere and magnetosphere, it is found that both the fluxes and the associated wave intensities are stable to external perturbations. However, if the ionosphere and magnetosphere are coupled through the ducting of the waves, a positive feedback may develop depending on the efficiency of the coupling. This result is a spiky, nonlinear precipitation pattern which for electrons has a period on the order of hundreds of seconds. A linear analysis that highlights the regions of instability is given, together with a computer simulation of the nonlinear regimes.
Baum, J. D.; Levine, J. N.
1980-01-01
The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.
Investigation of nonlinear effects in the instabilities and noise radiation of supersonic jets
Janjua, S. I.; McLaughlin, D. K.
1985-01-01
The nonlinear interactions of fluctuating components which produce noise in supersonic jet flows were studied experimentally. Attention was given to spectral components interactions and the spectral effects of increasing Re. A jet exhausted in perfectly expanded conditions was monitored by microphones in the maximum noise emission direction. Trials were run at Mach 1.4 and 2.1 and the Re was varied from 5000-20,000 and 9000-25,000, respectively. Hot-wire data were gathered to examine the mode-mode interactions and a point glow discharge was used to excite the jets. The noise was found to exhibit discrete frequency components and a single tone instability at Re below 10,000. Mode interactions were found to weaken after the instabilities reached a crescendo and then decayed, leading to a nonlinear spectral broadening effect.
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
Martinez, David
2015-11-01
We investigate on the National Ignition Facility (NIF) the ablative Rayleigh-Taylor (RT) instability in the transition from linear to highly nonlinear regimes. This work is part of the Discovery Science Program on NIF and of particular importance to indirect-drive inertial confinement fusion (ICF) where careful attention to the form of the rise to final peak drive is calculated to prevent the RT instability from shredding the ablator in-flight and leading to ablator mixing into the cold fuel. The growth of the ablative RT instability was investigated using a planar plastic foil with pre-imposed two-dimensional broadband modulations and diagnosed using x-ray radiography. The foil was accelerated for 12ns by the x-ray drive created in a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. The dependence on initial conditions was investigated by systematically changing the modulation amplitude, ablator material and the modulation pattern. For each of these cases bubble mergers were observed and the nonlinear evolution of the RT instability showed insensitivity to the initial conditions. This experiment provides critical data needed to validate current theories on the ablative RT instability for indirect drive that relies on the ablative stabilization of short-scale modulations for ICF ignition. This paper will compare the experimental data to the current nonlinear theories. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
Gianni, G; Paganini, E; Sello, S
2003-01-01
The onset of thermoacoustic instabilities in lean-premixed gas-turbine combustors is a crucial problem leading to degradation in engine and emissions performance and shortened component life. The main aim of this study is to propose a methodology based both on concepts of nonlinear dynamics and on geometric-topological invariants, for the characterization of attractors related to measurements based on the flame spontaneous light emission, like OH* radical, in order to classify different phases of the combustion process and to better recognize the transition mechanisms leading to the thermoacoustic instabilities. Preliminary results, clearly show the powerfulness of the approach to show the dynamical evolution of the flame and to evidence the onset of the thermoacoustic instabilities: in particular the topological invariant index (genus and related quantities) appear s as the best candidate for an early indicator of the dynamical transition, characterized by the onset of a more persistent, low entropy torus (q...
The Non-linear Saturation of the Goldreich-Schubert-Fricke Instability
Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey
2015-11-01
The Goldreich-Schubert-Fricke (GSF) instability is an important process in stellar interiors and possibly in exoplanetary atmospheres. While the linear phase of the instability has been explored for nearly fifty years, its non-linear saturation has not been explored in detail. The GSF is a double-diffusive instability in which Rayleigh unstable perturbations are robbed of buoyant stability by thermal diffusion. Here, we will present results from a suite of direct numerical simulations using the Spiegel-Veronis Boussinesq equations in the Dedalus framework. These DNS are designed to explore the behavior of the GSF over a range of Prandtl numbers. In stellar interiors, Pr ~=10-6 , but we are limited by computational resources to much higher values, so instead we will discuss the Pr scaling of transport and mixing. We will also discuss the impact of the Boussinesq approximation in the case where large aspect ration perturbations exceed a scale height.
ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Guo Boling; Zhang Jian
2008-01-01
This paper deals with a type of standing waves for the coupled nonlin-ear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1996-01-01
We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....
Chew, Huck Beng
2013-01-01
Determining the tractions along a surface or interface from measurement data in the far-fields of nonlinear materials is a challenging inverse problem which has significant engineering and nanoscience applications. Previously, a field projection method was established to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid (Hong and Kim, 2003. J. Mech. Phys. Solids 51, 1267). In this paper, the field projection method is further generalized to extracting the tractions along interfaces bounded by nonlinear materials, both with and without pre-existing cracks. The new formulation is based on Maxwell-Betti's reciprocal theorem with a reciprocity gap associated with nonlinear materials. We express the unknown normal and shear tractions along the interface in terms of the Fourier series, and use specially constructed analytical auxiliary fields in the reciprocal theorem to extract the unknown Fourier coefficients from far-field data; the reciprocity gap in the formulation is iteratively determined with a set of numerical algorithms. Our detailed numerical experiments demonstrate that this nonlinear field projection method (NFPM) is well-suited for extracting the interfacial tractions from the far-field data of any nonlinear elastic or elasto-plastic material with known constitutive laws. Applications of the NFPM to experiments and atomistic simulations are discussed.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Energy Technology Data Exchange (ETDEWEB)
Chang, Philip; Lamberts, Astrid [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Broderick, Avery E.; Shalaby, Mohamad [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Puchwein, Ewald, E-mail: chang65@uwm.edu [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom)
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
Haugen, Nils Erland L; Sannan, Sigurd
2010-01-01
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent non-linearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The non-linear code with the use of the AFM approach is validated against results from an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame, 146, 493-512 (2006)]. The numerical simulations are in accordance with the...
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-12-01
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
Dey, Pinkee; Suslov, Sergey A.
2016-12-01
A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.
Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium
Energy Technology Data Exchange (ETDEWEB)
Moatimid, Galal M., E-mail: gal-moa@hotmail.com [Department of Mathematics, Faculty of Education, Ain Shams University, Roxy (Egypt); Alali, Elham M. M., E-mail: dr-elham-alali@hotmail.com; Ali, Hoda S. M., E-mail: hoda-ali-1@hotmail.com [Department of Mathematics, Faculty of Science (Girls Branch), University of Tabuk, Tabuk, P.O. Box 741 (Saudi Arabia)
2014-09-15
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability
Pavan, J.; Ziebell, L. F.; Gaelzer, R.; Yoon, P. H.
2009-01-01
Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.
Non-linear Evolution of Rayleigh-Taylor Instability in a Radiation Supported Atmosphere
Jiang, Yan-Fei; Stone, James
2012-01-01
The non-linear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small scale structures are also suppressed in this case. In the non-linear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a variable Eddington tensor (VET) versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the non-linear development of RTI...
Nonlinear regime of the mode-coupling instability in 2D plasma crystals
Röcker, T B; Zhdanov, S K; Nosenko, V; Ivlev, A V; Thomas, H M; Morfill, G E
2014-01-01
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.
The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow
Clark, S E
2016-01-01
We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor-Couette flow. This is a multiscale perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor-Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg-Landau equation (GLE), while the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.
Delucia, James
We study various aspects of the linear and 2D (helically symmetric) nonlinear development of m = 1 resistive instabilities in the cylindrical spheromak. The cylindrical spheromak is a fictitious configuration in which the toroidal spheromak has been cut and straightened out to become a circular cylinder of radius a, length 2(pi)R, and with periodic boundary conditions. It has proven to be a usefull model for studying spheromak instabilities in which toroidal effects are not important. The majority of interest in this area lies in attempting to understand the effect that the resistive interchange instability has on confinement in the spheromak, the reason being that finite pressure spheromak configurations are always unstable to this mode. Therefore, most of the results presented in this thesis pertain to the nonlinear development of the resistive interchange mode. Our goal is to understand the quasilinear modifications of the equilibrium profile due to the growth of this instability, and the subsequent effect that the equilibrium modification has on the growth rate and eigenfunctions. Our studies of the resistive interchange mode reveal that mode saturation can occur due to the quasilinear flattening of the pressure profile in the vicinity of the mode rational surface. However, this saturation process is defeated when the plasma overheats and in regions of the plasma where the shear is low. Also, we found that fluid compression plays a significant, and optomistic role in the long term nonlinear development of this mode. Finally, in a tearing mode stable cylindrical spheromak configuration with an axial beta value of 6%, complete overlap of the m = 1 islands occurs in about 3% of the resistive skin time for a magnetic Reynold's number of S = 10('5). For typical parameters of the S-1 device at Princeton, this time corresponds to nearly one millisecond. We show that incorporation of the Hall terms into the resistive MHD model can stabilize the m = 1 resistive
Kinetic plasma turbulence during the nonlinear stage of the Kelvin-Helmholtz instability
Kemel, Koen; Lapenta, Giovanni; Califano, Francesco; Markidis, Stefano
2014-01-01
Using a full kinetic, implicit particle-in-cell code, iPiC3D, we studied the properties of plasma kinetic turbulence, such as would be found at the interface between the solar wind and the Earth magnetosphere at low latitude during northwards periods. In this case, in the presence of a magnetic field B oriented mostly perpendicular to the velocity shear, turbulence is fed by the disruption of a Kelvin-Helmholtz vortex chain via secondary instabilities, vortex pairing and non-linear interactions. We found that the magnetic energy spectral cascade between ion and electron inertial scales, $d_i$ and $d_e$, is in agreement with satellite observations and other previous numerical simulations; however, in our case the spectrum ends with a peak beyond $d_e$ due to the occurrence of the lower hybrid drift instability. The electric energy spectrum is influenced by effects of secondary instabilities: anomalous resistivity, fed by the development of the lower hybrid drift instability, steepens the spectral decay and, de...
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Gaur, Gurudatt; Das, Amita [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-07-15
The study of electron velocity shear driven instability in electron magnetohydrodynamics (EMHD) regime in three dimensions has been carried out. It is well known that the instability is non-local in the plane defined by the flow direction and that of the shear, which is the usual Kelvin-Helmholtz mode, often termed as the sausage mode in the context of EMHD. On the other hand, a local instability with perturbations in the plane defined by the shear and the magnetic field direction exists which is termed as kink mode. The interplay of these two modes for simple sheared flow case as well as that when an external magnetic field exists has been studied extensively in the present manuscript in both linear and nonlinear regimes. Finally, these instability processes have been investigated for the exact 2D dipole solutions of EMHD equations [M. B. Isichenko and A. N. Marnachev, Sov. Phys. JETP 66, 702 (1987)] for which the electron flow velocity is sheared. It has been shown that dipoles are very robust and stable against the sausage mode as the unstable wavelengths are typically longer than the dipole size. However, we observe that they do get destabilized by the local kink mode.
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
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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.
Nonlinear dynamics of beam-plasma instability in a finite magnetic field
Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.
2017-06-01
The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.
Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability.
Bosch, Pablo; Green, Stephen R; Lehner, Luis
2016-04-08
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordström-anti-de Sitter black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Energy Technology Data Exchange (ETDEWEB)
Ham, J. van; Beer, R.J. van; Builtjes, P.J.H.; Roemer, M.G.M. [TNO Inst. of Environmental Sciences, Delft (Netherlands); Koennen, G.P. [KNMI, Royal Netherlands Meteorological Inst., de Bilt (Netherlands); Oerlemans, J. [Utrecht Univ. (Netherlands). Inst. for Meteorological and Atmospheric Research
1995-12-31
In this presentation part of an investigation is described into risks for climate change which are presently not adequately covered in General Circulation Models. In the concept of climate change as a result of the enhanced greenhouse effect it is generally assumed that the radiative forcings from increased concentrations of greenhouse gases (GHG) will result in a proportional or quasilinear global warming. Though correlations of this kind are known from palaeoclimate research, the variability of the climate seems to prevent the direct proof of a causal relation between recent greenhouse gas concentrations and temperature observations. In order to resolve the issue the use of General Circulation Models (GCMs), though still inadequate at present, is indispensable. Around the world some 10 leading GCMs exist which have been the subject of evaluation and intercomparison in a number of studies. Their results are regularly assessed in the IPCC process. A discussion on their performance in simulating present or past climates and the causes of their weak points shows that the depiction of clouds is a major weakness of GCMs. A second element which is virtually absent in GCMs are the feedbacks from natural biogeochemical cycles. These cycles are influenced by man in a number of ways. GCMs have a limited performance in simulating regional effects on climate. Moreover, albedo instability, in part due to its interaction with cloudiness, is only roughly represented. Apparently, not all relevant processes have been included in the GCMs. That situation constitutes a risk, since it cannot be ruled out that a missing process could cause or trigger a non-linear climate change. In the study non-linear climate change is connected with those processes which could provide feedbacks with a risk for non-monotonous or discontinuous behaviour of the climate system, or which are unpredictable or could cause rapid transitions
The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability
Wang, Yanjin
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems.
Trillo, S; Gongora, J S Totero; Fratalocchi, A
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems
Trillo, S.
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Stormo, Arne; Lengliné, Olivier; Schmittbuhl, Jean; Hansen, Alex
2016-05-01
We compare experimental observations of a slow interfacial crack propagation along an heterogeneous interface to numerical simulations using a soft-clamped fiber bundle model. The model consists of a planar set of brittle fibers between a deformable elastic half-space and a rigid plate with a square root shape that imposes a non linear displacement around the process zone. The non-linear square-root rigid shape combined with the long range elastic interactions is shown to provide more realistic displacement and stress fields around the crack tip in the process zone and thereby significantly improving the predictions of the model. Experiments and model are shown to share a similar self-affine roughening of the crack front both at small and large scales and a similar distribution of the local crack front velocity. Numerical predictions of the Family-Viscek scaling for both regimes are discussed together with the local velocity distribution of the fracture front.
Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
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Saito, Shinji, E-mail: saito@stelab.nagoya-u.ac.jp [Graduate School of Science, Nagoya University, Nagoya (Japan); Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan); Nariyuki, Yasuhiro, E-mail: nariyuki@edu.u-toyama.ac.jp [Faculty of Human Development, University of Toyama, Toyama (Japan); Umeda, Takayuki, E-mail: umeda@stelab.nagoya-u.ac.jp [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan)
2015-07-15
A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
Mahdaoui, O.; Agassant, J.-F.; Laure, P.; Valette, R.; Silva, L.
2007-04-01
The polymer coextrusion process is a new method of sheet metal lining. It allows to substitute lacquers for steel protection in food packaging industry. The coextrusion process may exhibit flow instabilities at the interface between the two polymer layers. The objective of this study is to check the influence of processing and rheology parameters on the instabilities. Finite elements numerical simulations of the coextrusion allow to investigate various stable and instable flow configurations.
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
Ma, Jun; Qin, Hong; Yu, Zhi; Li, Dehui
2016-07-01
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB105003, 2013GB111000, 2014GB124005, 2015GB111003), National Natural Science Foundation of China (Nos. 11305171, 11405208), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328), the Science Foundation of the Institute of Plasma Physics, Chinese Academy of Sciences (DSJJ-15-JC02) and the CAS Program for the Interdisciplinary Collaboration Team
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.
Ryu, D; Frank, A I; Ryu, Dongsu; Frank, Adam
2000-01-01
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memo...
Nonlinear Evolution of the Radiation-Driven Magneto-Acoustic Instability (RMI)
Fernández, Rodrigo
2012-01-01
We examine the nonlinear development of unstable magnetosonic waves driven by a background radiative flux -- the Radiation-Driven Magneto-Acoustic Instability (RMI, a.k.a. the "photon bubble" instability). The RMI may serve as a persistent source of density, radiative flux, and magnetic field fluctuations in stably-stratified, optically-thick media. The conditions for instability are present in a variety of astrophysical environments, and do not require the radiation pressure to dominate or the magnetic field to be strong. Here we numerically study the saturation properties of the RMI, covering three orders of magnitude in the relative strength of radiation, magnetic field, and gas energies. Two-dimensional, time-dependent radiation-MHD simulations of local, stably-stratified domains are conducted with Zeus-MP in the optically-thick, highly-conducting limit. Our results confirm the theoretical expectations of Blaes and Socrates (2003) in that the RMI operates even in gas pressure-dominated environments that a...
NONLINEAR EVOLUTION OF THE RADIATION-DRIVEN MAGNETO-ACOUSTIC INSTABILITY
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Fernandez, Rodrigo; Socrates, Aristotle [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States)
2013-04-20
We examine the nonlinear development of unstable magnetosonic waves driven by a background radiative flux-the radiation-driven magneto-acoustic instability (RMI, a.k.a. the ''photon bubble'' instability). The RMI may serve as a persistent source of density, radiative flux, and magnetic field fluctuations in stably stratified, optically thick media. The conditions for instability are present in a variety of astrophysical environments and do not require the radiation pressure to dominate or the magnetic field to be strong. Here, we numerically study the saturation properties of the RMI, covering three orders of magnitude in the relative strength of radiation, magnetic field, and gas energies. Two-dimensional, time-dependent radiation-magnetohydrodynamic simulations of local, stably stratified domains are conducted with Zeus-MP in the optically thick, highly conducting limit. Our results confirm the theoretical expectations of Blaes and Socrates in that the RMI operates even in gas-pressure-dominated environments that are weakly magnetized. The saturation amplitude is a monotonically increasing function of the ratio of radiation to gas pressure. Keeping this ratio constant, we find that the saturation amplitude peaks when the magnetic pressure is comparable to the radiation pressure. We discuss the implications of our results for the dynamics of magnetized stellar envelopes, where the RMI should act as a source of sub-photospheric perturbations.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Dissipative parametric modulation instability and pattern formation in nonlinear optical systems
Perego, A. M.; Tarasov, N.; Churkin, D. V.; Turitsyn, S. K.; Staliunas, K.
2016-04-01
We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
Three-Dimensional Single-Mode Nonlinear Ablative Rayleigh-Taylor Instability
Yan, R.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.
2015-11-01
The nonlinear evolution of the ablative Rayleigh-Taylor (ART) instability is studied in three dimensions for conditions relevant to inertial confinement fusion targets. The simulations are performed using our newly developed code ART3D and an astrophysical code AstroBEAR. The laser ablation can suppress the growth of the short-wavelength modes in the linear phase but may enhance their growth in the nonlinear phase because of the vortex-acceleration mechanism. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the bubble velocity grows faster than predicted in the classical 3-D theory. When compared to 2-D results, 3-D short-wavelength bubbles grow faster and do not reach saturation. The unbounded 3-D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes into the ablated plasma filling the bubble volume. A density plateau is observed inside a nonlinear ART bubble and the plateau density is higher for shorter-wavelength modes. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Surface and interfacial creases in a bilayer tubular soft tissue
Razavi, Mir Jalil; Pidaparti, Ramana; Wang, Xianqiao
2016-08-01
Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as their morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability; therefore nonlinear finite element simulations are carried out to replicate the poststability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.
Laursen, Tod A
2003-01-01
This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Johansen, A; Johansen, Anders; Youdin, Andrew
2007-01-01
We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random wal...
The weakly nonlinear magnetorotational instability in a thin-gap Taylor-Couette flow
Clark, S E
2016-01-01
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a thin-gap, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We extend these results by performing a detailed force balance for the saturated azimuthal velocity and vertical magnetic field, demonstrating that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demons...
Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
Bondarescu, Ruxandra; Wasserman, Ira
2007-01-01
The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. Eventually, the system may reach thermal equilibrium and either (1) undergo a cyclic evolution with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of about $10^6$ years. Alternatively, a faster thermal runaway (timescale of about 100 ...
Delzanno, G. L.; Finn, J. M.; Lapenta, G.
2002-12-01
The nonlinear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column, is studied. A new cylindrical particle-in-cell code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a number of tests. The code is then used to compare the dynamics of three different models: the standard Euler or drift-Poisson model, the modified drift-Poisson model [J. Finn et al. Phys. Plasmas 6, 3744 (1999); Phys. Rev. Lett. 84, 2401 (2000)] with compressional effects, and the quasigeostrophic model of geophysical fluid dynamics in the limit of the γ-plane approximation. The results of this investigation show that Penning traps can be used to simulate geophysical fluids. Moreover, the results for the m=1 diocotron instability reproduce qualitatively the experiments [C. F. Driscoll, Phy. Rev. Lett. 64, 645 (1990); C. F. Driscoll et al. Phys. Fluids B 2, 1359 (1990)]: The instability turns the plasma "inside-out" resulting at the end in a stable, monotonic profile.
Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
Shtemler, Yuri M; Liverts, Edward
2014-01-01
The magneto-rotational decay instability (MRDI) of thin Keplerian discs threaded by poloidal magnetic fields is introduced and studied. The linear magnetohydrodynamic problem decouples into eigenvalue problems for in-plane slow- and fast- Alfv'een-Coriolis (AC), and vertical magnetosonic (MS) eigenmodes. The magnetorotational instability (MRI) is composed of a discrete number of unstable slow AC eigenmodes that is determined for each radius by the local beta. In the vicinity of the first beta threshold a parent MRI eigenmode together with a stable AC eigenmode (either slow or fast) and a stable MS eigenmode form a resonant triad. The three-wave MRDI relies on the nonlinear saturation of the parent MRI mode and the exponential growth of two daughter linearly stable waves, slow-AC and MS modes with an effective growth rate that is comparable to that of the parent MRI. If, however, the role of the AC daughter wave is played by a stable fast mode, all three modes remain bounded.
Abidate, Asmaa; Aniss, Said; Caballina, Ophélie; Souhar, Mohamed
2007-04-01
We report analytical results for the development of instability of an interface between two immiscible, Newtonian fluid layers confined in a rotating annular Hele-Shaw cell. We perform a linear stability analysis and focus our study on the influence of both Coriolis force and curvature parameters on the interface instability growth rate. The results show that the Coriolis force does not alter the stability of a disturbance with a particular wave number but reduces the maximum growth rate. The results related to the role played by the confinement of the liquid layers are also shown to provide a modification of the fastest-growing mode and its corresponding linear growth rate.
Yamasue, Kohei; Fukidome, Hirokazu; Funakubo, Kazutoshi; Suemitsu, Maki; Cho, Yasuo
2015-06-05
We investigate pristine and hydrogen-intercalated graphene synthesized on a 4H-SiC(0001) substrate by using noncontact scanning nonlinear dielectric potentiometry (NC-SNDP). Permanent dipole moments are detected at the pristine graphene-SiC interface. These originate from the covalent bonds of carbon atoms of the so-called buffer layer to the substrate. Hydrogen intercalation at the interface eliminates these covalent bonds and the original quasi-(6×6) corrugation, which indicates the conversion of the buffer layer into a second graphene layer by the termination of Si bonds at the interface. NC-SNDP images suggest that a certain portion of the Si dangling bonds remains even after hydrogen intercalation. These bonds are thought to act as charged impurities reducing the carrier mobility in hydrogen-intercalated graphene on SiC.
Yamasue, Kohei; Fukidome, Hirokazu; Funakubo, Kazutoshi; Suemitsu, Maki; Cho, Yasuo
2015-06-01
We investigate pristine and hydrogen-intercalated graphene synthesized on a 4 H -SiC (0001 ) substrate by using noncontact scanning nonlinear dielectric potentiometry (NC-SNDP). Permanent dipole moments are detected at the pristine graphene-SiC interface. These originate from the covalent bonds of carbon atoms of the so-called buffer layer to the substrate. Hydrogen intercalation at the interface eliminates these covalent bonds and the original quasi-(6 ×6 ) corrugation, which indicates the conversion of the buffer layer into a second graphene layer by the termination of Si bonds at the interface. NC-SNDP images suggest that a certain portion of the Si dangling bonds remains even after hydrogen intercalation. These bonds are thought to act as charged impurities reducing the carrier mobility in hydrogen-intercalated graphene on SiC.
Analytical model and MD simulation of nonlinear Richtmyer-Meshkov instability
Nishihara, Katsunobu; Abe, Motomi; Fukuda, Yuko; Zhakhovskii, Vasilii; Matsuoka, Chihiro
2001-10-01
We present two topics, an analytical model and moelrcular dynamic (MD) simulations of the Richtmyer-Meshokov instability (RMI). We have developled a selfconsistent analytical model that describes a nonlinear evolution of a vortex sheet in the two-dimensional RMI. The model consists of two kinematic boundary conditions, a modified Birkhoff-Rott equation and an equation for time evolution of circulation at the interface with a finite Atwood number. It is shown that the created vortcity on the interface has strong inhomogeneity, that causes locally streching and compression of the sheet. We discuss the dependence of the Atwood number on the nonlinear dynamics of the sheet. MD approache has been applied for converging shocks and RMI in a dense Lennard-Jones fluid in cylindrical geometry. MD method has fundamental advantages over hydrodymanic simulations such as no limitation of resolution in turbulent state. The appearance of Mach stems in the rippled shocks and turbulent mixing in RMI have been observed when the reflected shock passes through the unstable surface again. We discuss the mode number and Mach number dependence on the mixing.
Anderson, Miles; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G
2016-01-01
Localized dissipative structures (LDS) have been predicted to display a rich array of instabilities, yet systematic experimental studies have remained scarce. We have used a synchronously-driven optical fiber ring resonator to experimentally study LDS instabilities in the strong-driving regime of the AC-driven nonlinear Schr\\"odinger equation (also known as the Lugiato-Lefever model). Through continuous variation of a single control parameter, we have observed a string of theoretically predicted instability modes, including irregular oscillations and chaotic collapses. Beyond a critical point, we observe behaviour reminiscent of a phase transition: LDSs trigger localized domains of spatiotemporal chaos that invade the surrounding homogeneous state. Our findings directly confirm a number of theoretical predictions, and they highlight that complex LDS instabilities can play a role in experimental systems.
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
A note on nonlinear aspects of large-scale atmospheric instabilities
Energy Technology Data Exchange (ETDEWEB)
Wiin-Nielsen, A [The Royal Danish Academy of Sciences and Letters, Copenhagen (Denmark)
2001-04-01
A barotropic model with momentum transport, a simple baroclinic model with transports of heat only and a baroclinic model with both momentum and heat transports are used to illustrate the instabilities and the nonlinear longer term behavior of barotropic, baroclinic and mixed barotropic-baroclinic processes in models without forcing and frictional dissipation. While the instabilities of such models are well known thorough analytical studies of the linear perturbation equations, it is obvious that these studies give no information on the long term behavior which can be studied only by nonlinear equations. Numerical integration of low order nonlinear equations will be used to illustrate the long term behavior of the two models. The mains aspects of the observed atmospheric energy processes maybe reproduce by the most general low-order model used in this study give no information on the long term behavior, which can be studied only by nonlinear equations. Numerical integrations of low order nonlinear equations will be used to illustrate the long term behavior of the two models. The main aspects of the observed atmospheric energy processes may be reproduce by the most general low-order model used in this study. This model contains meridional transports of sensible heat and momentum by the Eddies which are included in the model. The reproduce the atmospheric energy diagram based on observational studies it is necessary to include heating and frictional dissipations. The latter two processes will be excluded in the present study in order to obtain the long term behavior is observed with rather large time scales. The most periodic variations are obtained from initial states with moderate values of the zonal parameters. [Spanish] Para ilustrar las inestabilidades y el comportamiento a largo plazo de procesos barotropicos-baroclinicos, mezclados en modelos sin disipaciones de friccion y forzamiento, se usan: un simple modelo baroclinico con transporte de momentum, un modelo
Institute of Scientific and Technical Information of China (English)
Xianqiong Zhong; Anping Xiang
2007-01-01
@@ The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinearity plays a role similar to the case of neglecting the group-velocity mismatch in modifying the modulation instability, namely, the positive and negative quintic nonlinearities can still enhance and weaken the modulation instability, respectively. The group-velocity mismatch can considerably change the gain spectrum of modulation instability in terms of its shape, peak value, and position. In the normal dispersion regime, with the increase of the group-velocity mismatch parameter,the gain spectrum widens and then narrows, shifts to higher frequencies, and the peak value gets higher before approaching a saturable value. In the abnormal dispersion regime, two separated spectra may occur when the group-velocity mismatch is taken into account. With the increase of the group-velocity mismatch parameter, the peak value of the gain spectrum gets higher and shorter before tending to a saturable value for the first and second spectral regimes, respectively.
Energy Technology Data Exchange (ETDEWEB)
Wabnitz, Stefan, E-mail: stefan.wabnitz@unibs.it [Dipartimento di Ingegneria dell' Informazione, Università degli Studi di Brescia, via Branze 38, 25123 Brescia (Italy); Wetzel, Benjamin [INRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Québec J3X 1S2 (Canada)
2014-07-25
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.
Takabatake, Fumi; Magome, Nobuyuki; Ichikawa, Masatoshi; Yoshikawa, Kenichi
2011-03-01
Spontaneous motion of a solid/liquid composite induced by a chemical Marangoni effect, where an oil droplet attached to a solid soap is placed on a water phase, was investigated. The composite exhibits various characteristic motions, such as revolution (orbital motion) and translational motion. The results showed that the mode of this spontaneous motion switches with a change in the size of the solid scrap. The essential features of this mode-switching were reproduced by ordinary differential equations by considering nonlinear friction with proper symmetry.
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj; Büchner, Jörg [Max Planck/Princeton Center for Plasma Physics, Göttingen (Germany); Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg-3, Göttingen (Germany)
2014-07-15
Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.
Korycansky, D. G.
1991-01-01
Two-dimensional nonlinear hydrodynamic calculations are presented which may help assess the effectiveness of the instability in transporting angular momentum in the equatorial zones of stars and planets which are stably stratified with respect to convection. The calculations were made by numerically integrating the 2D axisymmetric Navier-Stokes equations, including viscosity and heat conduction. The instability was followed into the nonlinear regime. The maximum rms velocity amplitude was found to correlate well with the product of the linear growth rate and radial length scale of the instability, consistent with the idea that the instability grows to an amplitude such that an eddy turnover time becomes equal to the growth time defined by the inverse of the growth rate. The time scale for angular momentum to be redistributed to a state of marginal stability was consistent with this picture. The results suggest that in physical situations a state of marginal stability will be maintained, since departures from such a state will be rapidly corrected.
Energy Technology Data Exchange (ETDEWEB)
Guo, Shimin, E-mail: gsm861@126.com [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands); Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049 (China); Sun, Anbang [Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands)
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
Sicolo, Sabrina; Fingerle, Mathias; Hausbrand, René; Albe, Karsten
2017-06-01
The chemical instability of the glassy solid electrolyte LiPON against metallic lithium and the occurrence of side reactions at their interface is investigated by combining a surface science approach and quantum-mechanical calculations. Using an evolutionary structure search followed by a melt-quenching protocol, a model for the disordered structure of LiPON is generated and put into contact with lithium. Even the static optimization of a simple model interface suggests that the diffusion of lithium into LiPON is driven by a considerable driving force that could easily take place under experimental conditions. Calculated reaction energies indicate that the reduction and decomposition of LiPON is thermodynamically favorable. By monitoring the evolution of the LiPON core levels as a function of lithium exposure, the disruption of the LiPON network alongside the occurrence of new phases is observed. The direct comparison between UV photoelectron spectroscopy measurements and calculated electronic densities of states for increasing stages of lithiation univocally identifies the new phases as Li2O, Li3P and Li3N. These products are stable against Li metal and form a passivation layer which shields the electrolyte from further decomposition while allowing for the diffusion of Li ions.
Nath, Sujit K
2016-01-01
We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks. It is known that molecular viscosity is negligible in accretion disks. Hence, it has been argued that Magnetorotational Instability (MRI) is responsible for transporting matter in the presence of weak magnetic field. However, there are some shortcomings, which question effectiveness of MRI. Now the question arises, whether other hydromagnetic effects, e.g. transient growth (TG), can play an important role to bring nonlinearity in the system, even at weak magnetic fields. Otherwise, whether MRI or TG, which is primarily responsible to reveal nonlinearity to make the flow turbulent? Our results prove explicitly that the flows with high Reynolds number (Re), which is the case of realistic astrophysical accretion disks, exhibit nonlinearity by best TG of perturbation modes faster than that by best modes producing MRI. For a fixed wavevector, MRI dominates over transient effects, only at low Re, lower than its value ...
Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
Barker, Adrian J; Ogilvie, Gordon I
2016-01-01
We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders $\\ell\\leq 5$, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when $\\frac{n}{\\Omega}\\lesssim -1$, where $n$ and $\\Omega$ are the orbital and spin angular freque...
Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander
2016-05-01
The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.
Bykov, Andrei M; Osipov, Sergei M; Vladimirov, Andrey E
2014-01-01
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (~eV) injected at the viscous subshock, to the escape of the highest energy CRs (~PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the d...
CSIR Research Space (South Africa)
Ojijo, Vincent O
2015-12-01
Full Text Available Polylactide (PLA) has inherent shortcomings that limit its widespread application: brittleness, slow crystallization rates, low melt strength and thermal instability during melt processing. In this paper, these problems are addressed through a...
Ji, Shanming; Yin, Jingxue; Cao, Yang
2016-11-01
In this paper, we consider the periodic problem for semilinear heat equation and pseudo-parabolic equation with logarithmic source. After establishing the existence of positive periodic solutions, we discuss the instability of such solutions.
Nonlinear Rayleigh--Taylor instability of the cylindrical fluid flow with mass and heat transfer
Indian Academy of Sciences (India)
ALY R SEADAWY; K EL-RASHIDY
2016-08-01
The nonlinear Rayleigh--Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg--Landau equation. The F-expansion method is used to get exactsolutions for a nonlinear Ginzburg--Landau equation. The region of solutions is displayed graphically.
Saleem, H.; Ali Shan, S.; Haque, Q.
2016-11-01
It is shown that the inhomogeneous field-aligned flow of heavier ions into the stationary plasma of the upper ionosphere produces very low frequency (of the order of a few Hz) electrostatic unstable ion acoustic waves (IAWs). This instability is an oscillatory instability unlike D'Angelo's purely growing mode. The growth rate of the ion acoustic wave (IAW) corresponding to heavier ions is due to shear flow and is larger than the ion Landau damping. However, the ion acoustic waves corresponding to non-flowing lighter ions are Landau damped. It is found that even if D'Angelo's instability condition is satisfied, the unstable mode develops its real frequency in this coupled system. Hence, the shear flow of one type of ions in a bi-ion plasma system produces ion acoustic wave activity. If the density non-uniformity is taken into account, then the drift wave becomes unstable. The coupled nonlinear equations for stationary ions "a," flowing ions "b," and inertialess electrons are also solved using the small amplitude limit. The solutions predict the existence of the order of a few kilometers electric field structures in the form of solitons and vortices, which is in agreement with the satellite observations.
Wan, Xiaoliang; Yu, Haijun; Weinan, E.
2015-05-01
In this work, we study the nonlinear instability of two-dimensional (2D) wall-bounded shear flows from the large deviation point of view. The main idea is to consider the Navier-Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to zero, the Freidlin-Wentzell (F-W) theory of large deviations defines the most probable transition path in the phase space, which is the minimizer of the F-W action functional and characterizes the development of the nonlinear instability subject to small random perturbations. Based on such a transition path we can define a critical Reynolds number for the nonlinear instability in the probabilistic sense. Then the action-based stability theory is applied to study the 2D Poiseuille flow in a short channel.
Energy Technology Data Exchange (ETDEWEB)
Qin, S.Q.; Jiao, J.J.; Tang, C.A.; Li, Z.G. [Chinese Academy of Sciences, Beijing (China)
2006-12-15
This paper studies the unstable mechanisms of the mechanical system that is composed of the stiff hosts (roof and floor) and the coal pillar using catastrophe theory. It is assumed that the roof is an elastic beam and the coal pillar is a strain-softening medium which can be described by the Weibull's distribution theory of strength. It is found that the instability leading to coal bump depends mainly on the system's stiffness ratio k, which is defined as the ratio of the flexural stiffness of the beam to the absolute value of the stiffness at the turning point of the constitutive curve of the coal pillar, and the homogeneity index m or shape parameter of the Weibull's distribution for the coal pillar. The applicability of the cusp catastrophe is demonstrated by applying the equations to the Mentougou coal mine. A non-linear dynamical model, which is derived by considering the time-dependent property of the coal pillar, is used to study the physical prediction of coal bumps. An algorithm of inversion for determining the parameters of the nonlinear dynamical model is suggested for seeking the precursory abnormality from the observed series of roof settlement. A case study of the Muchengjian coal mine is conducted and its nonlinear dynamical model is established from the observation series using the algorithm of inversion. An important finding is that the catastrophic characteristic index D (i.e., the bifurcation set of the cusp catastrophe model) drastically increases to a high peak value and then quickly drops close to instability. From the viewpoint of damage mechanics of coal pillar, a dynamical model of acoustic emission (AE) is established for modeling the AE activities in the evolutionary process of the system. It is revealed that the values of m and the evolutionary path (D = 0 or D not equal 0) of the system have a great impact on the AE activity patterns and characters.
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.
Wave instabilities in nonlinear Schrödinger systems with non vanishing background
Trillo, Stefano
2014-01-01
We investigate wave collapse in the generalized nonlinear Schrödinger (NLS) equation and in the presence of a non vanishing background. Through the use of virial identities, we establish a new criterion for blow-up.
Energy Technology Data Exchange (ETDEWEB)
Brunner, S. [Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, Ecole Polytechnique Fédérale de Lausanne, Lausanne, (Switzerland); Berger, R. L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Cohen, B. I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hausammann, L. [Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, Ecole Polytechnique Fédérale de Lausanne, Lausanne, (Switzerland); Valeo, E. J. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-10-01
Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPI accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
Identifying the active flow regions that drive linear and nonlinear instabilities
Marquet, Olivier
2015-01-01
A new framework for the analysis of unstable oscillator flows is explored. In linear settings, temporally growing perturbations in a non-parallel flow represent unstable eigenmodes of the linear flow operator. In nonlinear settings, self-sustained periodic oscillations of finite amplitude are commonly described as nonlinear global modes. In both cases the flow dynamics may be qualified as being endogenous, as opposed to the exogenous behaviour of amplifier flows driven by external forcing. This paper introduces the endogeneity concept, a specific definition of the sensitivity of the global frequency and growth rate with respect to variations of the flow operator. The endogeneity, defined both in linear and nonlinear settings, characterizes the contribution of localized flow regions to the global eigendynamics. It is calculated in a simple manner as the local point-wise inner product between the time derivative of the direct flow state and an adjoint mode. This study demonstrates for two canonical examples, th...
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Institute of Scientific and Technical Information of China (English)
Eric Tala-Tebue; Aurelien Kenfack-Jiotsa; Marius Hervé Tatchou-Ntemfack; Timoléon Crépin Kofané
2013-01-01
In this work,we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines.Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch.Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing.On one hand,the difference between the two lines induced the fission for only one mode of propagation.This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton,leading to a possible increasing of the bit rate.On the other hand,the dissymmetry of the two lines converts the network into a good amplifier for the w_ mode which corresponds to the regime admitting low frequencies.
Sheykhi, A.; Hajkhalili, S.
2015-11-01
We study topological dilaton black holes of Einstein gravity in the presence of exponential nonlinear electrodynamics. The event horizons of these black holes can be a two-dimensional positive, zero or negative constant curvature surface. We analyze thermodynamics of these solutions by calculating all conserved and thermodynamic quantities and showing that the first law holds on the black hole horizon. Then, we perform the stability analysis in both canonical and grand canonical ensemble and disclose the effects of the dilaton and nonlinear electrodynamics on the thermal stability of the solutions. Finally, we study the phase transition points of these black holes in the thermodynamic geometry approach.
Shvarts, D.; Oron, D.; Kartoon, D.; Rikanati, A.; Sadot, O.; Srebro, Y.; Yedvab, Y.; Ofer, D.; Levin, A.; Sarid, E.; Ben-Dor, G.; Erez, L.; Erez, G.; Yosef-Hai, A.; Alon, U.; Arazi, L.
2016-10-01
The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers (A) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h ~ α · A · gt2 with different values of a for the bubble and spike fronts. The RM mixing zone fronts evolve as h ~ tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin-Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.
Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
Gadelha, H.
2010-05-12
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
Energy Technology Data Exchange (ETDEWEB)
Carbajal, L., E-mail: L.Carbajal-Gomez@warwick.ac.uk; Cook, J. W. S. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Dendy, R. O. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, Oxfordshire (United Kingdom); Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Chapman, S. C. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Department of Mathematics and Statistics, University of Tromsø, N-9037, Tromsø (Norway); Max Planck Institute for the Physics of Complex Systems, D-01187, Dresden (Germany)
2014-01-15
The magnetoacoustic cyclotron instability (MCI) probably underlies observations of ion cyclotron emission (ICE) from energetic ion populations in tokamak plasmas, including fusion-born alpha-particles in JET and TFTR [Dendy et al., Nucl. Fusion 35, 1733 (1995)]. ICE is a potential diagnostic for lost alpha-particles in ITER; furthermore, the MCI is representative of a class of collective instabilities, which may result in the partial channelling of the free energy of energetic ions into radiation, and away from collisional heating of the plasma. Deep understanding of the MCI is thus of substantial practical interest for fusion, and the hybrid approximation for the plasma, where ions are treated as particles and electrons as a neutralising massless fluid, offers an attractive way forward. The hybrid simulations presented here access MCI physics that arises on timescales longer than can be addressed by fully kinetic particle-in-cell simulations and by analytical linear theory, which the present simulations largely corroborate. Our results go further than previous studies by entering into the nonlinear stage of the MCI, which shows novel features. These include stronger drive at low cyclotron harmonics, the re-energisation of the alpha-particle population, self-modulation of the phase shift between the electrostatic and electromagnetic components, and coupling between low and high frequency modes of the excited electromagnetic field.
Institute of Scientific and Technical Information of China (English)
PENG Miao-juan; CHENG Yu-min
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories.The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
Prediction of Nonlinear Evolution Character of Energetic-Particle-Driven Instabilities
Duarte, Vinicius; Gorelenkov, Nikolai; Heidbrink, William; Kramer, Gerrit; Nazikian, Raffi; Pace, David; Podesta, Mario; Tobias, Benjamin; Van Zeeland, Michael
2016-01-01
A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfv\\'enic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.
Directory of Open Access Journals (Sweden)
R. Mantovani
2002-01-01
Full Text Available This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energy-conversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant space-scales in the finite amplitude stage.
Misra, A P
2010-01-01
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schroedinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $\\beta\\propto\\lambda_C n_0^{1/3}$ (where $\\lambda_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\\gtrsim7\\times10^{33}$. It is also found that higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packet...
Institute of Scientific and Technical Information of China (English)
Zhong Xian-Qiong; Cheng Ke; Xiang An-Ping
2013-01-01
On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability (MI) have been analyzed and calculated for negative-refractive metamaterials (MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.
MD1831: Single Bunch Instabilities with Q" and Non-Linear Corrections
Carver, Lee Robert; De Maria, Riccardo; Li, Kevin Shing Bruce; Amorim, David; Biancacci, Nicolo; Buffat, Xavier; Maclean, Ewen Hamish; Metral, Elias; Lasocha, Kacper; Lefevre, Thibaut; Levens, Tom; Salvant, Benoit; CERN. Geneva. ATS Department
2017-01-01
During MD1751, it was observed that both a full single beam and 964 non-colliding bunches in Beam 1 (B1) and Beam 2 (B2) were both stable at the End of Squeeze (EOS) for 0A in the Landau Octupoles. At ß* = 40cm there is also a significant Q" arising from the lattice, as well as uncorrected non-linearities in the Insertion Regions (IRs). Each of these effects could be capable of fully stabilising the beam. This MD made first use of a Q" knob through variation of the Main Sextupoles (MS) by stabilising a single bunch at Flat Top, before showing at EOS that the non-linearities were the main contributors to the beam stability.
Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
Energy Technology Data Exchange (ETDEWEB)
Hendi, S.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Panah, B.E.; Momennia, M. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2016-03-15
Motivated by the violation of Lorentz invariance in quantum gravity, we study black hole solutions in gravity's rainbow in the context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain the related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered by an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate the thermal stability conditions for these black hole solutions in the context of canonical ensemble. We show that the thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge, and energy functions. (orig.)
Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
Hendi, Seyed Hossein; Panah, Behzad Eslam
2015-01-01
In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.
Nonlinear r-Modes in Neutron Stars Instability of an unstable mode
Gressman, P T; Suen, W M; Stergioulas, N; Friedman, J L; Gressman, Philip; Lin, Lap-Ming; Suen, Wai-Mo; Friedman, John L.
2002-01-01
We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.
On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations
Friedlander, Susan
2011-01-01
We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.
Heidari, Mohammad; Heidari, Ali; Homaei, Hadi
2014-01-01
The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.
Nonlinear Marangoni instability of a liquid jet in the presence of electric field
Energy Technology Data Exchange (ETDEWEB)
Zakaria, Kadry; Sirwah, Magdy A.; Assaf, Achmed [Tanta Univ. (Egypt). Dept. of Mathematics
2009-11-15
The work discusses the linear and nonlinear stability of cylindrical surface deformations between two incompressible fluids. The interface is carrying a uniform surface charge. The inner fluid is assumed to be a liquid jet. Both fluids are modeled as a special type of a Newtonian viscous fluid. Furthermore, the effect of surface adsorption is taken into account. Both fluids are assumed to be dielectric and the stability is discussed in the presence of a constant electric field in axial direction. The analysis is performed along the lines of a multiple scale perturbation expansion with additional slow time and space variables. The various stability criteria are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. The results show the dual role of the electric field and the negative rate of change of surface tension with the concentration of surfactant on the system stability, in both the linear and nonlinear steps. The nonlinear theory, when used to investigate the stability of liquid jet, appears accurately to predict new unstable regions. (orig.)
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
Jain, Neeraj
2016-01-01
The dissipation mechanism by which the magnetic field reconnects in the presence of an external (guide) magnetic field in the direction of the main current is not well understood. In thin electron current sheets (ECS) (thickness ~ an electron inertial length) formed in collisionless magnetic reconnection, electron shear flow instabilities (ESFI) are potential candidates for providing an anomalous dissipation mechanism which can break the frozen-in condition of the magnetic field affecting the structure and rate of reconnection. We investigate the evolution of ESFI in guide field magnetic reconnection. The properties of the resulting plasma turbulence and their dependence on the strength of the guide field are studied. Utilizing 3-D electron-magnetohydrodynamic simulations of ECS we show that, unlike the case of ECS self-consistently embedded in anti-parallel magnetic fields, the evolution of thin ECS in the presence of a guide field (equal to the asymptotic value of the reconnecting magnetic field or larger) ...
Non-linear aspects of Görtler instability in boundary layers with pressure gradient
Rogenski, J. K.; de Souza, L. F.; Floryan, J. M.
2016-12-01
The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.
A simplified nonlinear model of the Marangoni instability in gas absorption
Skurygin, E. F.; Poroyko, T. A.
2016-04-01
The process of gas absorption into initially motionless liquid layer is investigated. The convective instability caused by the temperature dependence of the surface tension. The critical time of transition of the process to unstable convective regime, as well as the intensity of mass transfer in a surface convection are estimated numerically. The mathematical model includes the equations of convective diffusion, thermal conduction and fluid motion. The problem was solved numerically in the two-dimensional formulation. In the coordinate along the interface the concentration of the absorbed substance is represented by three terms of the trigonometric Fourier series. A difference approximation of equations with an exponentially changing grid in the direction normal to the interface is used. The simulations results agree with the well-known experimental data on the absorption of carbon dioxide in water.
Choudhury, Prakriti Pal
2015-01-01
We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g., spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in halos critically depends on the ratio of the cooling time to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the prev...
Nonlinear ion dynamics in Hall thruster plasma source by ion transit-time instability
Lim, Youbong; Choe, Wonho; Mazouffre, Stéphane; Park, Jae Sun; Kim, Holak; Seon, Jongho; Garrigues, L.
2017-03-01
High-energy tail formation in an ion energy distribution function (IEDF) is explained in a Hall thruster plasma with the stationary crossed electric and magnetic fields whose discharge current is oscillated at the ion transit-time scale with a frequency of 360 kHz. Among ions in different charge states, singly charged Xe ions (Xe+) have an IEDF that is significantly broadened and shifted toward the high-energy side, which contributes to tail formation in the entire IEDF. Analytical and numerical investigations confirm that the IEDF tail is due to nonlinear ion dynamics in the ion transit-time oscillation.
Budroni, M. A.
2015-12-01
Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.
Yang, Li-Ping; Ding, Shun-Liang; Litak, Grzegorz; Song, En-Zhe; Ma, Xiu-Zhen
2015-01-01
The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.
Energy Technology Data Exchange (ETDEWEB)
Yang, Li-Ping, E-mail: yangliping302@hrbeu.edu.cn; Ding, Shun-Liang; Song, En-Zhe; Ma, Xiu-Zhen [Institute of Power and Energy Engineering, Harbin Engineering University, No. 145-1, Nantong Street, Nangang District, Harbin 150001 (China); Litak, Grzegorz [Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin (Poland)
2015-01-15
The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.
Yang, Li-Ping; Ding, Shun-Liang; Litak, Grzegorz; Song, En-Zhe; Ma, Xiu-Zhen
2015-01-01
The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.
Instability of wormholes supported by a ghost scalar field: II. Nonlinear evolution
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J A; Guzman, F S; Sarbach, O [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria, A P 2-82, 58040 Morelia, Michoacan (Mexico)
2009-01-07
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article, we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here, we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and those collapsing to a black hole, and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
Carlevaro, Nakia; Montani, Giovanni; Zonca, Fulvio
2015-01-01
In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analyzed.
Directory of Open Access Journals (Sweden)
B.S. Bhadauria
2014-02-01
Full Text Available The present paper deals with a weak nonlinear stability problem of magneto-convection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT along with internal heating effects. In the case of (ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Using Ginzburg-Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.
Hoelzl, M; Merkel, P; Atanasiu, C; Lackner, K; Nardon, E; Aleynikova, K; Liu, F; Strumberger, E; McAdams, R; Chapman, I; Fil, A
2014-01-01
The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realist...
Directory of Open Access Journals (Sweden)
Mohammad Heidari
2013-01-01
Full Text Available In this study, the static pull-in instability of beam-type micro-electromechanical system (MEMS is theoretically investigated. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two supervised neural networks, namely, back propagation (BP and radial basis function (RBF, have been used for modeling the static pull-in instability of microcantilever beam. These networks have four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data employed for training the networks and capabilities of the models in predicting the pull-in instability behavior has been verified. Based on verification errors, it is shown that the radial basis function of neural network is superior in this particular case and has the average errors of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations show a good agreement, which also proves the feasibility and effectiveness of the adopted approach.
Johansson, Magnus
2006-04-01
We analyze certain aspects of the classical dynamics of a one-dimensional discrete nonlinear Schrödinger model with inter-site as well as on-site nonlinearities. The equation is derived from a mixed Klein-Gordon/Fermi-Pasta-Ulam chain of anharmonic oscillators coupled with anharmonic inter-site potentials, and approximates the slow dynamics of the fundamental harmonic of discrete small-amplitude modulational waves. We give explicit analytical conditions for modulational instability of travelling plane waves, and find in particular that sufficiently strong inter-site nonlinearities may change the nature of the instabilities from long-wavelength to short-wavelength perturbations. Further, we describe thermodynamic properties of the model using the grand-canonical ensemble to account for two conserved quantities: norm and Hamiltonian. The available phase space is divided into two separated parts with qualitatively different properties in thermal equilibrium: one part corresponding to a normal thermalized state with exponentially small probabilities for large-amplitude excitations, and another part typically associated with the formation of high-amplitude localized excitations, interacting with an infinite-temperature phonon bath. A modulationally unstable travelling wave may exhibit a transition from one region to the other as its amplitude is varied, and thus modulational instability is not a sufficient criterion for the creation of persistent localized modes in thermal equilibrium. For pure on-site nonlinearities the created localized excitations are typically pinned to particular lattice sites, while for significant inter-site nonlinearities they become mobile, in agreement with well-known properties of localized excitations in Fermi-Pasta-Ulam-type chains.
Energy Technology Data Exchange (ETDEWEB)
Outeda, R.; D' Onofrio, A. [Grupo de Medios Porosos, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, C1063ACV Buenos Aires (Argentina); El Hasi, C.; Zalts, A. [Instituto de Ciencias, Universidad Nacional General Sarmiento, J. M. Gutiérrez 1150, B1613GSX, Los Polvorines, Provincia de Buenos Aires (Argentina)
2014-03-15
Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a color indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.
Hoelzl, M.; Huijsmans, G. T. A.; Merkel, P.; Atanasiu, C.; Lackner, K.; Nardon, E.; Aleynikova, K.; Liu, F.; Strumberger, E.; McAdams, R.; Chapman, I.; Fil, A.
2014-11-01
The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.
Energy Technology Data Exchange (ETDEWEB)
Ruyer, C., E-mail: charles.ruyer@polytechnique.edu; Gremillet, L., E-mail: laurent.gremillet@cea.fr; Debayle, A. [CEA, DAM, DIF, F-91297 Arpajon (France); Bonnaud, G. [CEA, Saclay, INSTN, F-91191 Gif-sur-Yvette (France)
2015-03-15
We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.
Ruyer, C; Debayle, A; Bonnaud, G
2015-01-01
We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.
DVI Film Flow Instability Based on the Normal Mode Analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Jae Young; Euh, Dong Jin [Handong Global Univ., Pohang (Korea, Republic of)
2013-10-15
In the present paper, as the first step of nonlinear studies, the appearance of the third order spatial differentiation of the film thickness in the wave propagation equation is to be derived. The two-fluid model in the adiabatic condition is employed and normal mode analysis. Interfacial pressure forces between steam and water need to be modeled for this purpose. n the present study, we developed a theoretical basis to study nonlinear wave phenomena on the DVI film flow which highly affect the DVI penetration and liquid droplets entrainment out. We set the hyperbolicity breaking condition by providing the interfacial pressure difference considering the curvature of the reactor vessel. The interfacial pressure difference could generate nonlinear wave such as the horseshoe wave which has been believed as a main source of film break up to produce huge amount of droplets to be entrained out. As a safety injection method, the direct vessel injection has been intensively developed in Korea and employed in the APR1400. The developing efforts were made from the determination of the number, location and size of DVI nozzles to the experimental demonstrations. Experimental facilities with various scales have shown its complicated phenomena due to highly nonlinear interaction between the steam and injected water flow. The injected DVI water forms a film type flow but very unstable due to the unsteady energetic steam flow which find the exits around the shell of the downcomer of the reactor vessel. This steam and liquid film interaction leads to the instability on the surface of the film flow and the waves are highly nonlinear to form undercutting, roll over, and finally droplet releasing. The entrained droplets causes a difficulty in the analysis to estimate the water penetrated into the reactor core to cool the nuclear fuels heated up. Unfortunately, these instabilities on the interface of the DVI liquid film have not been studied appropriately and the conservative
Energy Technology Data Exchange (ETDEWEB)
Casner, A., E-mail: alexis.casner@cea.fr; Masse, L.; Liberatore, S.; Loiseau, P.; Masson-Laborde, P. E.; Jacquet, L. [CEA, DAM, DIF, F-91297 Arpajon (France); Martinez, D.; Moore, A. S.; Seugling, R.; Felker, S.; Haan, S. W.; Remington, B. A.; Smalyuk, V. A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Farrell, M.; Giraldez, E.; Nikroo, A. [General Atomics, San Diego, California 92121 (United States)
2015-05-15
Academic tests in physical regimes not encountered in Inertial Confinement Fusion will help to build a better understanding of hydrodynamic instabilities and constitute the scientifically grounded validation complementary to fully integrated experiments. Under the National Ignition Facility (NIF) Discovery Science program, recent indirect drive experiments have been carried out to study the ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regime [A. Casner et al., Phys. Plasmas 19, 082708 (2012)]. In these experiments, a modulated package is accelerated by a 175 eV radiative temperature plateau created by a room temperature gas-filled platform irradiated by 60 NIF laser beams. The unique capabilities of the NIF are harnessed to accelerate this planar sample over much larger distances (≃1.4 mm) and longer time periods (≃12 ns) than previously achieved. This extended acceleration could eventually allow entering into a turbulent-like regime not precluded by the theory for the RTI at the ablation front. Simultaneous measurements of the foil trajectory and the subsequent RTI growth are performed and compared with radiative hydrodynamics simulations. We present RTI growth measurements for two-dimensional single-mode and broadband multimode modulations. The dependence of RTI growth on initial conditions and ablative stabilization is emphasized, and we demonstrate for the first time in indirect-drive a bubble-competition, bubble-merger regime for the RTI at ablation front.
Wang, Lei; Qi, Feng-Hua; Tang, Bing; Shi, Yu-Ying
2016-12-01
Under investigation in this paper is a variable-coefficient AB (vcAB) system, which describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. The modulation instability analysis of solutions with variable coefficients in the presence of a small perturbation is studied. The modified Darboux transformation (mDT) of the vcAB system is constructed via a gauge transformation. The first-order non-autonomous rogue wave solutions of the vcAB system are presented based on the mDT. It is found that the wave amplitude of B exhibits two types of structures, i.e. the double-peak structure appears if the plane-wave solution parameter ω is equal to zero, while selecting ω≠0 yields a single-peak one. Effects of the variable coefficients on the rogue waves are graphically discussed in detail. The periodic rogue wave and composite rogue wave are obtained with different inhomogeneous parameters. Additionally, the nonlinear tunneling of the rogue waves through a conventional hyperbolic nonlinear well and barrier are investigated.
Cain, A. B.; Thompson, M. W.
1986-01-01
The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.
2011-03-06
The PIs current research and development, funded by AFOSR, aims to develop novel means of vibration control for aerospace systems, system ... identification procedures for strongly nonlinear dynamical systems, and a fully passive limit cycle oscillation (LCO) suppression system for a model generic
Min, K.; Liu, K.; Gary, S. P.
2015-12-01
In the inner magnetosphere, the energy-dependent convection of ring current ions can lead to the ring-type proton velocity distributions with ∂fp(vperp)/∂vperp > 0 and ring speeds around the Alfvén speed. This ring-type velocity distribution is known to drive fast magnetosonic waves at propagation quasi-perpendicular to the background magnetic field B0 and, with sufficient temperature anisotropy, electromagnetic ion cyclotron (EMIC) waves at propagation parallel to B0. While there is an abundant literature on linear theory and computer simulations of EMIC waves driven by bi-Maxwellian ion distributions, the literature on the instabilities associated with ring-type proton velocity distributions in the inner magnetosphere is less substantial. Even less studied is the interplay of the two instabilities which lead to the growth of EMIC and fast magnetosonic waves, respectively. The goal of this paper is to provide a comprehensive picture of the instabilities responsible for the two types of waves and their interplay in the conditions of the inner magnetosphere, using linear dispersion theory and self-consistent particle-in-cell (PIC) simulations. For systematic analyses, two-component proton distributions fp = fr + fb are used, where fr represents a tenuous energetic proton velocity distribution with ∂fr(vperp)/∂vperp > 0 providing free energy and fb represents a dense Maxwellian background with sufficiently small beta corresponding to the inner magnetospheric condition. Both an ideal velocity ring and a partial shell with sinn-type pitch angle dependence will be considered for the fr component.
Franklin, Erick de Moraes
2016-01-01
Granular media are frequently found in nature and in industry and their transport by a fluid flow is of great importance to human activities. One case of particular interest is the transport of sand in open-channel and river flows. In many instances, the shear stresses exerted by the fluid flow are bounded to certain limits and some grains are entrained as bed-load: a mobile layer which stays in contact with the fixed part of the granular bed. Under these conditions, an initially flat granular bed may be unstable, generating ripples and dunes such as those observed on the bed of rivers. In free-surface water flows, dunes are bedforms that scale with the flow depth, while ripples do not scale with it. This article presents a model for the formation of ripples and dunes based on the proposition that ripples are primary linear instabilities and that dunes are secondary instabilities formed from the competition between the coalescence of ripples and free surface effects. Although simple, the model is able to expl...
Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays
Noskov, Roman E; Kivshar, Yuri S; 10.1103/PhysRevLett.108.093901
2012-01-01
We study modulational instability in nonlinear arrays of subwavelength metallic nanoparticles, and analyze numerically nonlinear scenarios of the instability development. We demonstrate that modulational instability can lead to the formation of regular periodic or quasi-periodic modulations of the polarization. We reveal that such nonlinear nanoparticle arrays can support long-lived standing and moving oscillating nonlinear localized modes - plasmon oscillons.
Hooper, E. B.; Sovinec, C. R.
2016-10-01
An instability observed in whole-device, resistive magnetohydrodynamic simulations of the driven phase of coaxial helicity injection in the National Spherical Torus eXperiment is identified as a current-driven resistive mode in an unusual geometry that transiently generates a current sheet. The mode consists of plasma flow velocity and magnetic field eddies in a tube aligned with the magnetic field at the surface of the injected magnetic flux. At low plasma temperatures (˜10-20 eV), the mode is benign, but at high temperatures (˜100 eV) its amplitude undergoes relaxation oscillations, broadening the layer of injected current and flow at the surface of the injected toroidal flux and background plasma. The poloidal-field structure is affected and the magnetic surface closure is generally prevented while the mode undergoes relaxation oscillations during injection. This study describes the mode and uses linearized numerical computations and an analytic slab model to identify the unstable mode.
Modulation instability: The beginning
Noskov, Roman; Belov, Pavel; Kivshar, Yuri
2012-11-01
The study of metal nanoparticles plays a central role in the emerging novel technologies employing optics beyond the diffraction limit. Combining strong surface plasmon resonances, high intrinsic nonlinearities and deeply subwavelength scales, arrays of metal nanoparticles offer a unique playground to develop novel concepts for light manipulation at the nanoscale. Here we suggest a novel principle to control localized optical energy in chains of nonlinear subwavelength metal nanoparticles based on the fundamental nonlinear phenomenon of modulation instability. In particular, we demonstrate that modulation instability can lead to the formation of long-lived standing and moving nonlinear localized modes of several distinct types such as bright and dark solitons, oscillons, and domain walls. We analyze the properties of these nonlinear localized modes and reveal different scenarios of their dynamics including transformation of one type of mode to another. We believe this work paves a way towards the development of nonlinear nanophotonics circuitry.
Secondary instabilities of linearly heated falling films
Institute of Scientific and Technical Information of China (English)
HU Jun; SUN Dejun; HU Guohui; YIN Xieyuan
2005-01-01
Secondary instabilities of linearly heated failing films are studied through three steps. Firstly, the analysis of the primary linear instability on Miladinova's long wave equation of the linearly heated film is performed. Secondly, the similar Landau equation is derived through weak nonlinear theory, and a two-dimensional nonlinear saturation solution of primary instability is obtained within the weak nonlinear domain. Thirdly, the secondary (three-dimensional) instability of the two-dimensional wave is studied by the Floquet theorem.Our secondary instability analysis shows that the Marangoni number has destabilization effect on the secondary instability.
Modulation instability: The beginning
Zakharov, V. E.; Ostrovsky, L. A.
2009-03-01
We discuss the early history of an important field of “sturm and drang” in modern theory of nonlinear waves. It is demonstrated how scientific demand resulted in independent and almost simultaneous publications by many different authors on modulation instability, a phenomenon resulting in a variety of nonlinear processes such as envelope solitons, envelope shocks, freak waves, etc. Examples from water wave hydrodynamics, electrodynamics, nonlinear optics, and convection theory are given.
Mathematical problems arising in interfacial electrohydrodynamics
Tseluiko, Dmitri
established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the
Extraction of temperature dependent interfacial resistance of thermoelectric modules
DEFF Research Database (Denmark)
Chen, Min
2011-01-01
This article discusses an approach for extracting the temperature dependency of the electrical interfacial resistance associated with thermoelectric devices. The method combines a traditional module-level test rig and a nonlinear numerical model of thermoelectricity to minimize measurement errors...... on the interfacial resistance. The extracted results represent useful data to investigating the characteristics of thermoelectric module resistance and comparing performance of various modules....
Extraction of temperature dependent interfacial resistance of thermoelectric modules
DEFF Research Database (Denmark)
Chen, Min
2011-01-01
This article discusses an approach for extracting the temperature dependency of the electrical interfacial resistance associated with thermoelectric devices. The method combines a traditional module-level test rig and a nonlinear numerical model of thermoelectricity to minimize measurement errors...
Midya, Samaresh; Duong, Alan; Thomas, Flint; Corke, Thomas
2016-11-01
Schoppa and Hussain (1998, 2002) demonstrated streak transient growth (STG) as the dominant streamwise coherent structure generation mechanism required for wall turbulence production. A novel, flush surface-mounted pulsed-DC plasma actuator was recently developed at the University of Notre Dame to actively intervene in STG. In recent high Reynolds number, zero pressure gradient turbulent boundary layer experiments, drag reduction of up to 68% was achieved. This is due to a plasma-induced near-wall, spanwise mean flow sufficient in magnitude to prevent the lift-up of low-speed streaks. This limits their flanking wall-normal component vorticity-a critical parameter in STG. Experiments also show that sufficiently large plasma-induced spanwise flow can exacerbate STG and increase drag by 80%. The ability to significantly increase or decrease drag by near-wall actuation provides an unprecedented new tool for clarifying the open questions regarding the interaction between near-wall coherent structures and those in the logarithmic region. In the reported experiments this interaction is experimentally characterized by a second-order Volterra nonlinear system model under both active suppression and enhancement of STG. Supported by NASA Langley under NNX16CL27C.
Nonlinear wavetrains in viscous conduits
Maiden, Michelle; Hoefer, Mark
2016-11-01
Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a deformable pipe forms. The long wave interfacial dynamics are well-described by a dispersive nonlinear partial differential equation. In this talk, experiments, numerics, and asymptotics of the viscous fluid conduit system will be presented. Structures at multiple length scales are discussed, including solitons, dispersive shock waves, and periodic waves. Modulations of periodic waves will be explored in the weakly nonlinear regime with the Nonlinear Schrödinger (NLS) equation. Modulational instability (stability) is identified for sufficiently short (long) periodic waves due to a change in dispersion curvature. These asymptotic results are confirmed by numerical simulations of perturbed nonlinear periodic wave solutions. Also, numerically observed are envelope bright and dark solitons well approximated by NLS. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
Zalian, Cyrus
2016-01-01
Context. The Blazhko effect, in RR Lyrae type stars, is a century old mystery. Dozens of theory exists, but none have been able to entirely reproduce the observational facts associated to this modulation phenomenon. Existing theory all rely on the usual continuous modelization of the star. Aims. We present a new paradigm which will not only explain the Blazhko effect, but at the same time, will give us alternative explanations to the red limit of the instability strip, the synchronization of layers, the mode selection and the existence of a limit cycle for radially pulsating stars. Methods. We describe the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators. Considering a spatial discretisation of the star, supposing a spherical symmetry, we develop the equation of motion and energy up to the third order in the radial and adiabatic case. Then, we include the influence of the ionization region as a relaxation oscillator by including elements from synchronisation theory. Results. This dis...
Prediction of Algebraic Instabilities
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Interfacial effects in multilayers
Energy Technology Data Exchange (ETDEWEB)
Barbee, T.W. Jr. [Lawrence Livermore National Lab., CA (United States). Chemistry and Materials Science Dept.
1998-12-31
Interfacial structure and the atomic interactions between atoms at interfaces in multilayers or nano-laminates have significant impact on the physical properties of these materials. A technique for the experimental evaluation of interfacial structure and interfacial structure effects is presented and compared to experiment. In this paper the impact of interfacial structure on the performance of x-ray, soft x-ray and extreme ultra-violet multilayer optic structures is emphasized. The paper is concluded with summary of these results and an assessment of their implications relative to multilayer development and the study of buried interfaces in solids in general.
Long-Wavelength Rupturing Instability in Surface-Tension-Driven Benard Convection
Swift, J. B.; Hook, Stephen J. Van; Becerril, Ricardo; McCormick, W. D.; Swinney, H. L.; Schatz, Michael F.
1999-01-01
A liquid layer with a free upper surface and heated from below is subject to thermocapillary-induced convective instabilities. We use very thin liquid layers (0.01 cm) to significantly reduce buoyancy effects and simulate Marangoni convection in microgravity. We observe thermocapillary-driven convection in two qualitatively different modes, short-wavelength Benard hexagonal convection cells and a long-wavelength interfacial rupturing mode. We focus on the long-wavelength mode and present experimental observations and theoretical analyses of the long-wavelength instability. Depending on the depths and thermal conductivities of the liquid and the gas above it, the interface can rupture downwards and form a dry spot or rupture upwards and form a high spot. Linear stability theory gives good agreement to the experimental measurements of onset as long as sidewall effects are taken into account. Nonlinear theory correctly predicts the subcritical nature of the bifurcation and the selection between the dry spot and high spots.
Pattern formation and mass transfer under stationary solutal Marangoni instability.
Schwarzenberger, Karin; Köllner, Thomas; Linde, Hartmut; Boeck, Thomas; Odenbach, Stefan; Eckert, Kerstin
2014-04-01
According to the seminal theory by Sternling and Scriven, solutal Marangoni convection during mass transfer of surface-active solutes may occur as either oscillatory or stationary instability. With strong support of Manuel G. Velarde, a combined initiative of experimental works, in particular to mention those of Linde, Wierschem and coworkers, and theory has enabled a classification of dominant wave types of the oscillatory mode and their interactions. In this way a rather comprehensive understanding of the nonlinear evolution of the oscillatory instability could be achieved. A comparably advanced state-of-the-art with respect to the stationary counterpart seemed to be out of reach a short time ago. Recent developments on both the numerical and experimental side, in combination with assessing an extensive number of older experiments, now allow one to draw a more unified picture. By reviewing these works, we show that three main building blocks exist during the nonlinear evolution: roll cells, relaxation oscillations and relaxation oscillations waves. What is frequently called interfacial turbulence results from the interaction between these partly coexisting basic patterns which may additionally occur in different hierarchy levels. The second focus of this review lies on the practical importance of such convection patterns concerning their influence on mass transfer characteristics. Particular attention is paid here to the interaction between Marangoni and buoyancy effects which frequently complicates the pattern formation even more. To shed more light on these dependencies, new simulations regarding the limiting case of stabilizing density stratification and vanishing buoyancy are incorporated.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Interfacial fluid dynamics and transport processes
Schwabe, Dietrich
2003-01-01
The present set of lectures and tutorial reviews deals with various topical aspects related to instabilities of interfacial processes and driven flows from both the theoretical and experimental point of views. New research has been spurred by the many demands for applications in material sciences (melting, solidification, electro deposition), biomedical engineering and processing in microgravity environments. This book is intended as both a modern source of reference for researchers in the field as well as an introduction to postgraduate students and non-specialists from related areas.
Emulsions for interfacial filtration.
Energy Technology Data Exchange (ETDEWEB)
Grillet, Anne Mary; Bourdon, Christopher Jay; Souza, Caroline Ann; Welk, Margaret Ellen; Hartenberger, Joel David; Brooks, Carlton, F.
2006-11-01
We have investigated a novel emulsion interfacial filter that is applicable for a wide range of materials, from nano-particles to cells and bacteria. This technology uses the interface between the two immiscible phases as the active surface area for adsorption of targeted materials. We showed that emulsion interfaces can effectively collect and trap materials from aqueous solution. We tested two aqueous systems, a bovine serum albumin (BSA) solution and coal bed methane produced water (CBMPW). Using a pendant drop technique to monitor the interfacial tension, we demonstrated that materials in both samples were adsorbed to the liquid-liquid interface, and did not readily desorb. A prototype system was built to test the emulsion interfacial filter concept. For the BSA system, a protein assay showed a progressive decrease in the residual BSA concentration as the sample was processed. Based on the initial prototype operation, we propose an improved system design.
Evaporative Instability in Binary Mixtures
Narayanan, Ranga; Uguz, Erdem
2012-11-01
In this talk we depict the physics of evaporative convection for binary systems in the presence of surface tension gradient effects. Two results are of importance. The first is that a binary system, in the absence of gravity, can generate an instability only when heated from the vapor side. This is to be contrasted with the case of a single component where instability can occur only when heated from the liquid side. The second result is that a binary system, in the presence of gravity, will generate an instability when heated from either the vapor or the liquid side provided the heating is strong enough. In addition to these results we show the conditions at which interfacial patterns can occur. Support from NSF OISE 0968313, Partner Univ. Fund and a Chateaubriand Fellowship is acknowledged.
Equilibrium Electro-osmotic Instability
Rubinstein, Isaak
2014-01-01
Since its prediction fifteen years ago, electro-osmotic instability has been attributed to non-equilibrium electro-osmosis related to the extended space charge which develops at the limiting current in the course of concentration polarization at a charge-selective interface. This attribution had a double basis. Firstly, it has been recognized that equilibrium electro-osmosis cannot yield instability for a perfectly charge-selective solid. Secondly, it has been shown that non-equilibrium electro-osmosis can. First theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge-selectivity for the sake of simplicity and so did the subsequent numerical studies of various time-dependent and nonlinear features of electro-osmotic instability. In this letter, we show that relaxing the assumption of perfect charge-selectivity (tantamount to fixing the electrochemical potential in the solid) allows for equilibrium electro-osmotic instability. Moreover, we s...
Gravitational Instabilities in Circumstellar Disks
Kratter, Kaitlin M
2016-01-01
[Abridged] Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability, and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability, supplemented with a survey of numerical simulations that aim to capture the non-linear evolution. We emphasize the role of thermodynamics and large scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analyt...
Abelianization of QCD plasma instabilities
Arnold, Peter; Lenaghan, Jonathan
2004-12-01
QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what nonlinear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities in the nonlinear regime may have close parallels to similar processes in traditional plasma physics. We conjecture that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge theory becomes equivalent, respectively, to (i) traditional plasma physics, which is U(1) gauge theory, and (ii) plasma physics of U(1)×U(1) gauge theory.
Interfacial gauge methods for incompressible fluid dynamics.
Saye, Robert
2016-06-01
Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.
Nonlinear chemoconvection in the methylene-blue-glucose system: Two-dimensional shallow layers
Pons, A. J.; Batiste, O.; Bees, M. A.
2008-07-01
Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue-glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.
Krysinski, Tomasz
2013-01-01
This book presents a study of the stability of mechanical systems, i.e. their free response when they are removed from their position of equilibrium after a temporary disturbance. After reviewing the main analytical methods of the dynamical stability of systems, it highlights the fundamental difference in nature between the phenomena of forced resonance vibration of mechanical systems subjected to an imposed excitation and instabilities that characterize their free response. It specifically develops instabilities arising from the rotor-structure coupling, instability of control systems, the se
Energy Technology Data Exchange (ETDEWEB)
K.Y. Ng
2003-08-25
The lecture covers mainly Sections 2.VIII and 3.VII of the book ''Accelerator Physics'' by S.Y. Lee, plus mode-coupling instabilities and chromaticity-driven head-tail instability. Besides giving more detailed derivation of many equations, simple interpretations of many collective instabilities are included with the intention that the phenomena can be understood more easily without going into too much mathematics. The notations of Lee's book as well as the e{sup jwt} convention are followed.
Corona-induced electrohydrodynamic instabilities in low conducting liquids
Energy Technology Data Exchange (ETDEWEB)
Vega, F.; Perez, A.T. [Depto. Electronica y Electromagnetismo, Facultad de Fisica, Universidad de Sevilla, Avda. Reina Mercedes, s/n. 41012, Sevilla (Spain)
2003-06-01
The rose-window electrohydrodynamic (EHD) instability has been observed when a perpendicular field with an additional unipolar ion injection is applied onto a low conducting liquid surface. This instability has a characteristic pattern with cells five to 10 times greater than those observed in volume instabilities caused by unipolar injection. We have used corona discharge from a metallic point to perform some measurements of the rose-window instability in low conducting liquids. The results are compared to the linear theoretical criterion for an ohmic liquid. They confirmed that the minimum voltage for this instability is much lower than that for the interfacial instability in high conducting liquids. This was predicted theoretically in the dependence of the critical voltage as a function of the non-dimensional conductivity. It is shown that in a non-ohmic liquid the rose window appears as a secondary instability after the volume instability. (orig.)
Beam Instabilities in the Scale Free Regime
Folli, Viola; Conti, Claudio; 10.1103/PhysRevLett.108.033901
2012-01-01
The instabilities arising in a one-dimensional beam sustained by the diffusive photorefractive nonlinearity in out-of-equilibrium ferroelectrics are theoretically and numerically investigated. In the "scale-free model", in striking contrast with the well-known spatial modulational instability, two different beam instabilities dominate: a defocusing and a fragmenting process. Both are independent of the beam power and are not associated to any specific periodic pattern.
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W -shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W -shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
Vector-Resonance-Multimode Instability
Sergeyev, S. V.; Kbashi, H.; Tarasov, N.; Loiko, Yu.; Kolpakov, S. A.
2017-01-01
The modulation and multimode instabilities are the main mechanisms which drive spontaneous spatial and temporal pattern formation in a vast number of nonlinear systems ranging from biology to laser physics. Using an Er-doped fiber laser as a test bed, here for the first time we demonstrate both experimentally and theoretically a new type of a low-threshold vector-resonance-multimode instability which inherits features of multimode and modulation instabilities. The same as for the multimode instability, a large number of longitudinal modes can be excited without mode synchronization. To enable modulation instability, we modulate the state of polarization of the lasing signal with the period of the beat length by an adjustment of the in-cavity birefringence and the state of polarization of the pump wave. As a result, we show the regime's tunability from complex oscillatory to periodic with longitudinal mode synchronization in the case of resonance matching between the beat and cavity lengths. Apart from the interest in laser physics for unlocking the tunability and stability of dynamic regimes, the proposed mechanism of the vector-resonance-multimode instability can be of fundamental interest for the nonlinear dynamics of various distributed systems.
Sahu, K. C.; Matar, O. K.
2010-11-01
The three-dimensional linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. We focus on the parameter ranges for which Squire's theorem for the two-layer Newtonian problem does not exist. The modified Orr-Sommerfeld and Squire equations in each layer are derived and solved using an efficient spectral collocation method. Our results demonstrate the presence of three-dimensional instabilities for situations where the square root of the viscosity ratio is larger than the thickness ratio of the two layers; these "interfacial" mode instabilities are also present when density stratification is destabilizing. These results may be of particular interest to researchers studying the transient growth and nonlinear stability of two-fluid non-Newtonian flows. We also show that the "shear" modes, which are present at sufficiently large Reynolds numbers, are most unstable to two-dimensional disturbances.
Modulational instability of short pulses in long optical fibers
DEFF Research Database (Denmark)
Shukla, P. K.; Juul Rasmussen, Jens
1986-01-01
The effect of time-derivative nonlinearity is incorporated into the study of the modulational instability of heat pulses propagating through long optical fibers. Conditions for soliton formation are discussed......The effect of time-derivative nonlinearity is incorporated into the study of the modulational instability of heat pulses propagating through long optical fibers. Conditions for soliton formation are discussed...
INSTABILITY OF TRAVELING WAVES OF THE KURAMOTO-SIVASHINSKY EQUATION
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Consider any traveling wave solution of the Kuramoto-Sivashinsky equation that is asymptotic to a constant as x → +∞. The authors prove that it is nonlinearly unstable under H1perturbations. The proof is based on a general theorem in Banach spaces asserting that linear instability implies nonlinear instability.
Non-contact atomic-level interfacial force microscopy
Energy Technology Data Exchange (ETDEWEB)
Houston, J.E.; Fleming, J.G.
1997-02-01
The scanning force microscopies (notably the Atomic Force Microscope--AFM), because of their applicability to nearly all materials, are presently the most widely used of the scanning-probe techniques. However, the AFM uses a deflection sensor to measure sample/probe forces which suffers from an inherent mechanical instability that occurs when the rate of change of the force with respect to the interfacial separation becomes equal to the spring constant of the deflecting member. This instability dramatically limits the breadth of applicability of AFM-type techniques to materials problems. In the course of implementing a DOE sponsored basic research program in interfacial adhesion, a self-balancing force sensor concept has been developed and incorporated into an Interfacial Force Microscopy (IFM) system by Sandia scientists. This sensor eliminates the instability problem and greatly enhances the applicability of the scanning force-probe technique to a broader range of materials and materials parameters. The impact of this Sandia development was recognized in 1993 by a Department of Energy award for potential impact on DOE programs and by an R and D 100 award for one of the most important new products of 1994. However, in its present stage of development, the IFM is strictly a research-level tool and a CRADA was initiated in order to bring this sensor technology into wide-spread availability by making it accessible in the form of a commercial instrument. The present report described the goals, approach and results of this CRADA effort.
Liu, Wanhai; Yu, Changping; Jiang, Hongbin; Li, Xinliang
2017-02-01
Based on the harmonic analysis [Liu et al., Phys. Plasmas 22, 112112 (2015)], the analytical investigation on the harmonic evolution in Rayleigh-Taylor instability (RTI) at a spherical interface has been extended to the general case of arbitrary Atwood numbers by using the method of the formal perturbation up to the third order in a small parameter. Our results show that the radius of the initial interface [i.e., Bell-Plessett (BP) effect] dramatically influences the harmonic evolution for arbitrary Atwood numbers. When the initial radius approaches infinity compared against the initial perturbation wavelength, the amplitudes of the first four harmonics will recover those in planar RTI. The BP effect makes the amplitudes of the zeroth, second, and third harmonics increase faster for a larger Atwood number than smaller one. The BP effect reduces the third-order negative feedback to the fundamental mode for a smaller Atwood number, and strengthens it for a larger one. Hence, the BP effect helps the fundamental mode grow faster for a smaller Atwood number.
Gravitational Instabilities in Circumstellar Disks
Kratter, Kaitlin; Lodato, Giuseppe
2016-09-01
Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review, we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small-scale turbulence-like density fluctuations, and fragmentation of the disk itself. We present the analytic theory that describes the linear growth phase of the instability supplemented with a survey of numerical simulations that aim to capture the nonlinear evolution. We emphasize the role of thermodynamics and large-scale infall in controlling the outcome of the instability. Despite apparent controversies in the literature, we show a remarkable level of agreement between analytic predictions and numerical results. In the next part of our review, we focus on the astrophysical consequences of the instability. We show that the disks most likely to be gravitationally unstable are young and relatively massive compared with their host star, Md/M*≥0.1. They will develop quasi-stable spiral arms that process infall from the background cloud. Although instability is less likely at later times, once infall becomes less important, the manifestations of the instability are more varied. In this regime, the disk thermodynamics, often regulated by stellar irradiation, dictates the development and evolution of the instability. In some cases the instability may lead to fragmentation into bound companions. These companions are more likely to be brown dwarfs or stars than planetary mass objects. Finally, we highlight open questions related to the development of a turbulent cascade in thin disks and the role of mode-mode coupling in setting the maximum angular
Interfacial solvation thermodynamics
Ben-Amotz, Dor
2016-10-01
Previous studies have reached conflicting conclusions regarding the interplay of cavity formation, polarizability, desolvation, and surface capillary waves in driving the interfacial adsorptions of ions and molecules at air-water interfaces. Here we revisit these questions by combining exact potential distribution results with linear response theory and other physically motivated approximations. The results highlight both exact and approximate compensation relations pertaining to direct (solute-solvent) and indirect (solvent-solvent) contributions to adsorption thermodynamics, of relevance to solvation at air-water interfaces, as well as a broader class of processes linked to the mean force potential between ions, molecules, nanoparticles, proteins, and biological assemblies.
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Effect of nanoscale patterned interfacial roughness on interfacial toughness.
Energy Technology Data Exchange (ETDEWEB)
Zimmerman, Jonathan A.; Moody, Neville Reid; Mook, William M. (University of Minnesota, Minneapolis, MN); Kennedy, Marian S. (Clemson University, Clemson, SC); Bahr, David F. (Washington State University, Pullman, WA); Zhou, Xiao Wang; Reedy, Earl David, Jr.
2007-09-01
The performance and the reliability of many devices are controlled by interfaces between thin films. In this study we investigated the use of patterned, nanoscale interfacial roughness as a way to increase the apparent interfacial toughness of brittle, thin-film material systems. The experimental portion of the study measured the interfacial toughness of a number of interfaces with nanoscale roughness. This included a silicon interface with a rectangular-toothed pattern of 60-nm wide by 90-nm deep channels fabricated using nanoimprint lithography techniques. Detailed finite element simulations were used to investigate the nature of interfacial crack growth when the interface is patterned. These simulations examined how geometric and material parameter choices affect the apparent toughness. Atomistic simulations were also performed with the aim of identifying possible modifications to the interfacial separation models currently used in nanoscale, finite element fracture analyses. The fundamental nature of atomistic traction separation for mixed mode loadings was investigated.
DEFF Research Database (Denmark)
D'Angelo, N.
1967-01-01
A recombination instability is considered which may arise in a plasma if the temperature dependence of the volume recombination coefficient, alpha, is sufficiently strong. Two cases are analyzed: (a) a steady-state plasma produced in a neutral gas by X-rays or high energy electrons; and (b) an af...
Compressible instability of rapidly expanding spherical material interfaces
Mankbadi, Mina Reda
The focus herein is on the instability of a material interface formed during an abrupt release of concentrated energy as in detonative combustion, explosive dispersals, and inertial-confinement fusion. These applications are modeled as a spherical shock-tube in which high-pressure gas initially contained in a small spherical shell is suddenly released. A forward-moving shock and an inward-moving secondary shock are formed, and between them a material interface develops that separates high-density fluid from the low-density one. The wrinkling of this interface controls mixing and energy release. The interface's stability is studied with and without the inclusion of metalized particulates. A numerical scheme is developed to discretize the full nonlinear equations of the base flow, and the 3D linearized perturbed flow equations. Linearization is followed by spherical harmonic decomposition of the disturbances, thereby reducing the 3D computational domain to one-dimensional radial domain. The 3D physical nature of the disturbances is maintained throughout the procedure. An extended Roe-Pike scheme coupled with a WENO scheme is developed to capture the discontinuities and accurately predict the disturbances. In Chapter 2, the contact interface's stability is analyzed in the inviscid single-phase. The disturbances grow exponentially and the growth rate is insensitive to the radial initial-disturbance profile. For wave numbers less than 100, the results are in accordance with previous theories but clarify that compressibility reduces the growth rate. Unlike the classical RTI, the growth rate reaches saturation at high wavenumbers. The parametric studies show that for specific ratios of initial pressure and temperature, the instability can be eliminated altogether. Chapter 3 discusses the full effects of viscosity and thermal diffusivity. Although Prandtl number effects are minimal, viscous effects dampen the high-wave numbers. For a given Reynolds number there is a peak
Hydromagnetic Instabilities in Neutron Stars
Lasky, Paul D; Kokkotas, Kostas D; Glampedakis, Kostas
2011-01-01
We model the non-linear ideal magnetohydrodynamics of poloidal magnetic fields in neutron stars in general relativity assuming a polytropic equation of state. We identify familiar hydromagnetic modes, in particular the 'sausage/varicose' mode and 'kink' instability inherent to poloidal magnetic fields. The evolution is dominated by the kink instability, which causes a cataclysmic reconfiguration of the magnetic field. The system subsequently evolves to new, non-axisymmetric, quasi-equilibrium end-states. The existence of this branch of stable quasi-equilibria may have consequences for magnetar physics, including flare generation mechanisms and interpretations of quasi-periodic oscillations.
Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil
Wei, Tao; Duan, Fei
2016-12-01
We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent linear stability analysis, it is found that the interface instability is enhanced by vapor recoil with time using an effective growth rate. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension, and the effects of the latter are not asymptotically negligible near rupture, reflected by a rescaled effective interfacial pressure. A two-dimensional nonlinear evolution is investigated for the quasi-equilibrium evaporating layers with different evaporative conditions for Rayleigh-Taylor unstable and sessile layers. For weak mass loss and strong vapor recoil, the well-defined capillary ridges emerge around a deepening narrow valley with increasing wavelength under a positive gravity, while, on the basis of initial condition, main and secondary droplets are either coalesced partially or separated by a sharp dry-out point under a negative gravity. The rupture location depends strongly on the characteristics of a given initial condition, except for the random perturbation. For both the cases, an increase in the modified evaporation number tends to reduce the rupture time tr and droplet thickness remarkably. Similarity analysis along with numerical strategy is presented for the final stage of touch-down dynamics, determined by a physical balance between the vapor recoil and capillary force. The evaporation-driven rupture with a significant vapor recoil and negligible mass loss is shown to contain a countably infinite number of similarity solutions whose horizontal and vertical length scales behave as (tr - t)1/2 and (tr - t)1/3. The first similarity solution represents a stable single-point rupture.
Mizuno, Yosuke; Lyubarsky, Yuri; ishikawa, Ken-Ichi; Hardee, Philip E.
2010-01-01
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the non-linear regime nearly ceases for increasing magnetic pitch.
Mode-locking via dissipative Faraday instability
Tarasov, Nikita; Perego, Auro M.; Churkin, Dmitry V.; Staliunas, Kestutis; Turitsyn, Sergei K.
2016-08-01
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system--spectrally dependent losses--achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.
Mode-locking via dissipative Faraday instability.
Tarasov, Nikita; Perego, Auro M; Churkin, Dmitry V; Staliunas, Kestutis; Turitsyn, Sergei K
2016-08-09
Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system-spectrally dependent losses-achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.
Redeker, J; Vogt, P M
2011-01-01
Carpal instability can be understood as a disturbed anatomical alignment between bones articulating in the carpus. This disturbed balance occurs either only dynamically (with movement) under the effect of physiological force or even statically at rest. The most common cause of carpal instability is wrist trauma with rupture of the stabilizing ligaments and adaptive misalignment following fractures of the radius or carpus. Carpal collapse plays a special role in this mechanism due to non-healed fracture of the scaphoid bone. In addition degenerative inflammatory alterations, such as chondrocalcinosis or gout, more rarely aseptic bone necrosis of the lunate or scaphoid bones or misalignment due to deposition (Madelung deformity) can lead to wrist instability. Under increased pressure the misaligned joint surfaces lead to bone arrosion with secondary arthritis of the wrist. In order to arrest or slow down this irreversible process, diagnosis must occur as early as possible. Many surgical methods have been thought out to regain stability ranging from direct reconstruction of the damaged ligaments, through ligament replacement to partial stiffening of the wrist joint.
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Instability of supersymmetric microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Interfacial forces in aqueous media
van Oss, Carel J
2006-01-01
Thoroughly revised and reorganized, the second edition of Interfacial Forces in Aqueous Media examines the role of polar interfacial and noncovalent interactions among biological and nonbiological macromolecules as well as biopolymers, particles, surfaces, cells, and both polar and apolar polymers. The book encompasses Lifshitz-van der Waals and electrical double layer interactions, as well as Lewis acid-base interactions between colloidal entities in polar liquids such as water. New in this Edition: Four previously unpublished chapters comprising a new section on interfacial propertie
FINANCIAL INSTABILITY AND POLITICAL INSTABILITY
Directory of Open Access Journals (Sweden)
Ionescu Cristian
2012-12-01
Full Text Available There is an important link between the following two variables: financial instability and political instability. Often, the link is bidirectional, so both may influence each other. This is way the lately crisis are becoming larger and increasingly complex. Therefore, the academic environment is simultaneously talking about economic crises, financial crises, political crises, social crises, highlighting the correlation and causality between variables belonging to the economic, financial, political and social areas, with repercussions and spillover effects that extend from one area to another. Given the importance, relevance and the actuality of the ones described above, I consider that at least a theoretical analysis between economic, financial and political factors is needed in order to understand the reality. Thus, this paper aims to find links and connections to complete the picture of the economic reality.
Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation
Risler, Thomas
2013-01-01
Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In a previous work (Basan et al., Phys. Rev. Lett. 106, 158101 (2011)), we demonstrated that an instability arising from viscous shear stresses caused by the constant flow due to cell turnover in the epithelium could drive this phenomenon. While interfacial tension between the two tissues as well as mechanical resistance of the stroma tend to maintain a flat interface, an instability occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Here, extensions of this work are presented, where cell division in the epithelium is coupled to the local concentration of nutrients or growth factors diffusing from the stroma. This enhances the instability by a mechanism similar to that of the Mullins-Sekerka instability in single...
High temperature interfacial superconductivity
Bozovic, Ivan [Mount Sinai, NY; Logvenov, Gennady [Port Jefferson Station, NY; Gozar, Adrian Mihai [Port Jefferson, NY
2012-06-19
High-temperature superconductivity confined to nanometer-scale interfaces has been a long standing goal because of potential applications in electronic devices. The spontaneous formation of a superconducting interface in bilayers consisting of an insulator (La.sub.2CuO.sub.4) and a metal (La.sub.1-xSr.sub.xCuO.sub.4), neither of which is superconducting per se, is described. Depending upon the layering sequence of the bilayers, T.sub.c may be either .about.15 K or .about.30 K. This highly robust phenomenon is confined to within 2-3 nm around the interface. After exposing the bilayer to ozone, T.sub.c exceeds 50 K and this enhanced superconductivity is also shown to originate from a 1 to 2 unit cell thick interfacial layer. The results demonstrate that engineering artificial heterostructures provides a novel, unconventional way to fabricate stable, quasi two-dimensional high T.sub.c phases and to significantly enhance superconducting properties in other superconductors. The superconducting interface may be implemented, for example, in SIS tunnel junctions or a SuFET.
Stability Theory for Interfacial Patterns in Magnetic Pulse Welding
Nassiri, Ali; Chini, Gregory; Kinsey, Brad; UNH Team
2013-11-01
Magnetic Pulse Welding (MPW) is a solid state, high strain-rate joining process in which a weld of dissimilar or similar materials can be created via high-speed oblique impact of two workpieces. Experiments routinely show the emergence of a distinctive wavy pattern, with a well defined amplitude and wavelength of approximately 20 and 70 micrometers, respectively, at the interface between the two welded materials. Although the origin of the wavy pattern has been the subject of much investigation, a unique fundamental physical theory for this phenomenon is as yet not widely accepted. Some researchers have proposed that the interfacial waves are formed in a process akin to Kelvin-Helmholtz instability, with relative shear movement of the flyer and base plates providing the energy source. Here, we employ a linear stability analysis to investigate whether the wavy pattern could be the signature of a shear-driven high strain-rate instability of an elastic-plastic solid material. Preliminary results confirm that an instability giving rise to a wavy interfacial pattern is possible.
Visco-Resistive Plasmoid Instability
Comisso, Luca
2016-01-01
The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as $S^{1/4} {\\left( {1 + {P_m}} \\right)}^{-5/8}$ and $S^{3/8} {\\left( {1 + {P_m}} \\right)}^{-3/16}$ with respect to the Lundquist number $S$ and the magnetic Prandtl number $P_m$. Furthermore, the linear layer width is shown to scale as $S^{-1/8} {(1+P_m)}^{1/16}$. The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime. In particular, the time-scale of the nonlinear growth of the plasmoids is found to be $\\tau_{NL} \\sim S^{-3/16} {(1 + P_m)^{19/32}}{\\tau _{A,L}}$. The nonlinear growth of the plasmoids is radically different from the linear one and it is shown to be essential to understand the global current sheet disruption. It is also discussed how the plasmoid instability enables fast magnetic reconnection in visco-resistive plasmas. In particular, it is shown t...
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
The subcritical baroclinic instability in local accretion disc models
Lesur, G
2009-01-01
(abridged) Aims: We present new results exhibiting a subcritical baroclinic instability (SBI) in local shearing box models. We describe the 2D and 3D behaviour of this instability using numerical simulations and we present a simple analytical model describing the underlying physical process. Results: A subcritical baroclinic instability is observed in flows stable for the Solberg-Hoiland criterion using local simulations. This instability is found to be a nonlinear (or subcritical) instability, which cannot be described by ordinary linear approaches. It requires a radial entropy gradient weakly unstable for the Schwartzchild criterion and a strong thermal diffusivity (or equivalently a short cooling time). In compressible simulations, the instability produces density waves which transport angular momentum outward with typically alpha<3e-3, the exact value depending on the background temperature profile. Finally, the instability survives in 3D, vortex cores becoming turbulent due to parametric instabilities...
Energy Technology Data Exchange (ETDEWEB)
Deng Mingxi [College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Wang Ping [College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Lv Xiafu [College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China)
2006-07-21
This paper describes influences of interfacial properties on second-harmonic generation of Lamb waves propagating in layered planar structures. The nonlinearity in the elastic wave propagation is treated as a second-order perturbation of the linear elastic response. Due to the kinematic nonlinearity and the elastic nonlinearity of materials, there are second-order bulk and surface/interface driving sources in layered planar structures through which Lamb waves propagate. These driving sources can be thought of as forcing functions of a series of double frequency lamb waves (DFLWs) in terms of the approach of modal expansion analysis for waveguide excitation. The total second-harmonic fields consist of a summation of DFLWs in the corresponding stress-free layered planar structures. The interfacial properties of layered planar structures can be described by the well-known finite interfacial stiffness technique. The normal and tangential interfacial stiffness constants can be coupled with the equation governing the expansion coefficient of each DFLW component. On the other hand, the normal and tangential interfacial stiffness constants are associated with the degree of dispersion between Lamb waves and DFLWs. Theoretical analyses and numerical simulations indicate that the efficiency of second-harmonic generation by Lamb wave propagation is closely dependent on the interfacial properties of layered structures. The potential of using the effect of second-harmonic generation by Lamb wave propagation to characterize the interfacial properties of layered structures are considered. Some experimental results are presented.
Laboratory blast wave driven instabilities
Kuranz, Carolyn
2008-11-01
This presentation discusses experiments involving the evolution of hydrodynamic instabilities in the laboratory under high-energy-density (HED) conditions. These instabilities are driven by blast waves, which occur following a sudden, finite release of energy, and consist of a shock front followed by a rarefaction wave. When a blast wave crosses an interface with a decrease in density, hydrodynamic instabilities will develop. Instabilities evolving under HED conditions are relevant to astrophysics. These experiments include target materials scaled in density to the He/H layer in SN1987A. About 5 kJ of laser energy from the Omega Laser facility irradiates a 150 μm plastic layer that is followed by a low-density foam layer. A blast wave structure similar to those in supernovae is created in the plastic layer. The blast wave crosses an interface having a 2D or 3D sinusoidal structure that serves as a seed perturbation for hydrodynamic instabilities. This produces unstable growth dominated by the Rayleigh-Taylor (RT) instability in the nonlinear regime. We have detected the interface structure under these conditions using x-ray backlighting. Recent advances in our diagnostic techniques have greatly improved the resolution of our x-ray radiographic images. Under certain conditions, the improved images show some mass extending beyond the RT spike and penetrating further than previously observed or predicted by current simulations. The observed effect is potentially of great importance as a source of mass transport to places not anticipated by current theory and simulation. I will discuss the amount of mass in these spike extensions, the associated uncertainties, and hypotheses regarding their origin We also plan to show comparisons of experiments using single mode and multimode as well as 2D and 3D initial conditions. This work is sponsored by DOE/NNSA Research Grants DE-FG52-07NA28058 (Stewardship Sciences Academic Alliances) and DE-FG52-04NA00064 (National Laser User
Amplitude Equation for Instabilities Driven at Deformable Surfaces - Rosensweig Instability
Pleiner, Harald; Bohlius, Stefan; Brand, Helmut R.
2008-11-01
The derivation of amplitude equations from basic hydro-, magneto-, or electrodynamic equations requires the knowledge of the set of adjoint linear eigenvectors. This poses a particular problem for the case of a free and deformable surface, where the adjoint boundary conditions are generally non-trivial. In addition, when the driving force acts on the system via the deformable surface, not only Fredholm's alternative in the bulk, but also the proper boundary conditions are required to get amplitude equations. This is explained and demonstrated for the normal field (or Rosensweig) instability in ferrofluids as well as in ferrogels. An important aspect of the problem is its intrinsic dynamic nature, although at the end the instability is stationary. The resulting amplitude equation contains cubic and quadratic nonlinearities as well as first and (in the gel case) second order time derivatives. Spatial variations of the amplitudes cannot be obtained by using simply Newell's method in the bulk.
Direct Numerical Simulation of Three-Dimensional Richtmyer-Meshkov Instability
Institute of Scientific and Technical Information of China (English)
FU De-Xun; MA Yan-Wen; LI Xin-Liang
2008-01-01
Direct numerical simulation(DNS)is used to study flow characteristics after interaction of a planar shock with a spherical media interface in each side of which the density is different.This interfacial instability is known as the Richtmyer-Meshkov(R-M)instability.The compressible Nayier-Stoke equations are discretized with group velocity control(GVC)modified fourth order accurate compact difference scheme.Three-dimensional numerical simulations are performed for R-M instability installed passing a shock through a spherical interface.Based on numerical results the characteristics of 3D R-M instability are analysed.The evaluation for distortion of the interface.the deformation of the incident shock wave and effects of refraction,reflection and diffraction are Dresented.The effects of the interfacial instability on produced vorticity and mixing is discussed.
Modulational instability arising from collective Rayleigh scattering.
Robb, G R M; McNeil, B W J
2003-02-01
It is shown that under certain conditions a collection of dielectric Rayleigh particles suspended in a viscous medium and enclosed in a bidirectional ring cavity pumped by a strong laser field can produce a new modulational instability transverse to the wave-propagation direction. The source of the instability is collective Rayleigh scattering i.e., the spontaneous formation of periodic longitudinal particle-density modulations and a backscattered optical field. Using a linear stability analysis a dispersion relation is derived which determines the region of parameter space in which modulational instability of the backscattered field and the particle distribution occurs. In the linear regime the pump is modulationally stable. A numerical analysis is carried out to observe the dynamics of the interaction in the nonlinear regime. In the nonlinear regime the pump field also becomes modulationally unstable and strong pump depletion occurs.
Controlling and minimizing fingering instabilities in non-Newtonian fluids.
Fontana, João V; Dias, Eduardo O; Miranda, José A
2014-01-01
The development of the viscous fingering instability in Hele-Shaw cells has great practical and scientific importance. Recently, researchers have proposed different strategies to control the number of interfacial fingering structures, or to minimize as much as possible the amplitude of interfacial disturbances. Most existing studies address the situation in which an inviscid fluid displaces a viscous Newtonian fluid. In this work, we report on controlling and minimizing protocols considering the situation in which the displaced fluid is a non-Newtonian, power-law fluid. The necessary changes on the controlling schemes due to the shear-thinning and shear thickening nature of the displaced fluid are calculated analytically and discussed.
Numerical simulation of the hydrodynamic instability experiments and flow mixing
Institute of Scientific and Technical Information of China (English)
BAI JingSong; WANG Tao; LI Ping; ZOU LiYong; LIU CangLi
2009-01-01
Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI), a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly, the MVPPM code is verified and validated by simulating three instability cases: The first one is a Riemann problem of viscous flow on the shock tube;the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability, which is conducted on the AWE's shock tube. By comparing the numerical results with experimental data, good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models accelerated by explosion products of a gaseous explosive mixture (GEM), which are adopted in our experiments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces, and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer experiment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface, and presents the displacement of front face of jelly layer, bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images, and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely, especially at late times.
Numerical simulation of the hydrodynamic instability experiments and flow mixing
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on the numerical methods of volume of fluid (VOF) and piecewise parabolic method (PPM) and parallel circumstance of Message Passing Interface (MPI),a parallel multi-viscosity-fluid hydrodynamic code MVPPM (Multi-Viscosity-Fluid Piecewise Parabolic Method) is developed and performed to study the hydrodynamic instability and flow mixing. Firstly,the MVPPM code is verified and validated by simulating three instability cases:The first one is a Riemann problem of viscous flow on the shock tube; the second one is the hydrodynamic instability and mixing of gaseous flows under re-shocks; the third one is a half height experiment of interfacial instability,which is conducted on the AWE’s shock tube. By comparing the numerical results with experimental data,good agreement is achieved. Then the MVPPM code is applied to simulate the two cases of the interfacial instabilities of jelly models acceler-ated by explosion products of a gaseous explosive mixture (GEM),which are adopted in our experi-ments. The first is implosive dynamic interfacial instability of cylindrical symmetry and mixing. The evolving process of inner and outer interfaces,and the late distribution of mixing mass caused by Rayleigh-Taylor (RT) instability in the center of different radius are given. The second is jelly layer ex-periment which is initialized with one periodic perturbation with different amplitude and wave length. It reveals the complex processes of evolution of interface,and presents the displacement of front face of jelly layer,bubble head and top of spike relative to initial equilibrium position vs. time. The numerical results are in excellent agreement with that experimental images,and show that the amplitude of initial perturbations affects the evolvement of fluid mixing zone (FMZ) growth rate extremely,especially at late times.
Dentin-cement Interfacial Interaction
Atmeh, A.R.; Chong, E.Z.; Richard, G.; Festy, F.; Watson, T.F.
2012-01-01
The interfacial properties of a new calcium-silicate-based coronal restorative material (Biodentine™) and a glass-ionomer cement (GIC) with dentin have been studied by confocal laser scanning microscopy (CLSM), scanning electron microscopy (SEM), micro-Raman spectroscopy, and two-photon auto-fluorescence and second-harmonic-generation (SHG) imaging. Results indicate the formation of tag-like structures alongside an interfacial layer called the “mineral infiltration zone”, where the alkaline caustic effect of the calcium silicate cement’s hydration products degrades the collagenous component of the interfacial dentin. This degradation leads to the formation of a porous structure which facilitates the permeation of high concentrations of Ca2+, OH-, and CO32- ions, leading to increased mineralization in this region. Comparison of the dentin-restorative interfaces shows that there is a dentin-mineral infiltration with the Biodentine, whereas polyacrylic and tartaric acids and their salts characterize the penetration of the GIC. A new type of interfacial interaction, “the mineral infiltration zone”, is suggested for these calcium-silicate-based cements. PMID:22436906
Interfacial behavior of polymer electrolytes
Energy Technology Data Exchange (ETDEWEB)
Kerr, John; Kerr, John B.; Han, Yong Bong; Liu, Gao; Reeder, Craig; Xie, Jiangbing; Sun, Xiaoguang
2003-06-03
Evidence is presented concerning the effect of surfaces on the segmental motion of PEO-based polymer electrolytes in lithium batteries. For dry systems with no moisture the effect of surfaces of nano-particle fillers is to inhibit the segmental motion and to reduce the lithium ion transport. These effects also occur at the surfaces in composite electrodes that contain considerable quantities of carbon black nano-particles for electronic connection. The problem of reduced polymer mobility is compounded by the generation of salt concentration gradients within the composite electrode. Highly concentrated polymer electrolytes have reduced transport properties due to the increased ionic cross-linking. Combined with the interfacial interactions this leads to the generation of low mobility electrolyte layers within the electrode and to loss of capacity and power capability. It is shown that even with planar lithium metal electrodes the concentration gradients can significantly impact the interfacial impedance. The interfacial impedance of lithium/PEO-LiTFSI cells varies depending upon the time elapsed since current was turned off after polarization. The behavior is consistent with relaxation of the salt concentration gradients and indicates that a portion of the interfacial impedance usually attributed to the SEI layer is due to concentrated salt solutions next to the electrode surfaces that are very resistive. These resistive layers may undergo actual phase changes in a non-uniform manner and the possible role of the reduced mobility polymer layers in dendrite initiation and growth is also explored. It is concluded that PEO and ethylene oxide-based polymers are less than ideal with respect to this interfacial behavior.
Nonconservative higher-order hydrodynamic modulation instability
Kimmoun, O.; Hsu, H. C.; Kibler, B.; Chabchoub, A.
2017-08-01
The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy sidebands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary sidebands generate an infinite number of additional sidebands, forming a triangular sideband cascade. After saturation, it is expected that the system experiences a return to initial conditions followed by a spectral recurrence dynamics. Much complex nonlinear wave field motion is expected, when the secondary or successive sideband pair that is created is also located in the finite instability gain range around the main carrier frequency peak. This latter process is referred to as higher-order MI. We report a numerical and experimental study that confirms observation of higher-order MI dynamics in water waves. Furthermore, we show that the presence of weak dissipation may counterintuitively enhance wave focusing in the second recurrent cycle of wave amplification. The interdisciplinary weakly nonlinear approach in addressing the evolution of unstable nonlinear waves dynamics may find significant resonance in other nonlinear dispersive media in physics, such as optics, solids, superfluids, and plasma.
Model of oscillatory instability in vertically-homogeneous atmosphere
Directory of Open Access Journals (Sweden)
P. B. Rutkevich
2009-02-01
Full Text Available Existence and repeatability of tornadoes could be straightforwardly explained if there existed instability, responsible for their formation. However, it is well known that convection is the only instability in initially stable air, and the usual convective instability is not applicable for these phenomena. In the present paper we describe an instability in the atmosphere, which can be responsible for intense vortices. This instability appears in a fluid with Coriolis force and dissipation and has oscillatory behaviour, where the amplitude growth is accompanied by oscillations with frequency comparable to the growth rate of the instability. In the paper, both analytical analysis of the linear phase of the instability and nonlinear simulation of the developed stage of the air motion are addressed. This work was supported by the RFBR grant no. 09-05-00374-a.
Strong electron-scale instability in relativistic shear flows
Alves, Eduardo Paulo; Grismayer, Thomas; Fonseca, Ricardo; Silva, Luis
2013-10-01
Collisionless shear-driven plasma instabilities have recently been shown to be capable of generating strong and large-scale magnetic fields and may therefore play an important role in relativistic astrophysical outflows. We present a new collisionless shear-driven plasma instability, which operates in the plane transverse to the Kelvin Helmholtz instability (KHI). We develop the linear stability analysis of electromagnetic modes in the transverse plane and find that the growth rate of this instability is greater than the competing KHI in relativistic shears. The analytical results are confirmed with 2D particle-in-cell (PIC) simulations. Simulations also reveal the nonlinear evolution of the instability which leads to the development of mushroom-like electron-density structures, similar to the Rayleigh Taylor instability. Finally, the interplay between the competing instabilities is investigated in 3D PIC simulations.
Institute of Scientific and Technical Information of China (English)
Peng ZHANG; Yunhui DU; Hanwu LIU; Daben ZENG; Jianzhong CUI; Limin BA
2004-01-01
At room temperature, the rolling treatment of steel-mushy Al-7graphite bonding plate was carried out under different relative reduction. The influence of rolling on interfacial mechanical property of this bonding plate was studied. The results show that, for steel-mushy Al-7graphite bonding plate which is made up of 1.2 mm in thickness 08Al steel plate and 2.0 mm in thickness Al-7graphite layer, there is a nonlinear relationship between interfacial shear strength of bonding plate and relative reduction of rolling. When relative reduction of rolling is smaller than 2.59%, with the increasing of relative reduction, interfacial shear strength of bonding plate increases gradually. When relative reduction of rolling is bigger than 2.59%, with the increasing of relative reduction, interfacial shear strength of bonding plate decreases continuously. When relative reduction of rolling is 2.59%, the largest interfacial shear strength 77.0 MPa can be obtained.
Torsional instability in suspension bridges: The Tacoma Narrows Bridge case
Arioli, Gianni; Gazzola, Filippo
2017-01-01
All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific community. We suggest a new nonlinear model for a suspension bridge and we perform numerical experiments with the parameters corresponding to the collapsed Tacoma Narrows Bridge. We show that the thresholds of instability are in line with those observed the day of the collapse. Our analysis enables us to give a new explanation for the torsional instability, only based on the nonlinear behavior of the structure.
Magnetorotational Explosive Instability in Keplerian Disks
Shtemler, Yuri; Mond, Michael
2015-01-01
In this paper it is shown that deferentially rotating disks that are in the presence of weak axial magnetic field are prone to a new nonlinear explosive instability. The latter occurs due to the near-resonance three-wave interactions of a magnetorotational instability with stable Alfven-Coriolis and magnetosonic modes. The dynamical equations that govern the temporal evolution of the amplitudes of the three interacting modes are derived. Numerical solutions of the dynamical equations indicate that small frequency mismatch gives rise to two types of behavior: 1. explosive instability which leads to infinite values of the three amplitudes within a finite time, and 2. bounded irregular oscillations of all three amplitudes. Asymptotic solutions of the dynamical equations are obtained for the explosive instability regimes and are shown to match the numerical solutions near the explosion time.
Self-focusing instability of two-dimensional solitons and vortices
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Juul Rasmussen, J.
1995-01-01
The instability of two-dimensional solitons and vortices is demonstrated in the framework of the three-dimensional nonlinear Schrodinger equation (NLSE). The instability can be regarded as the analog of the Kadomtsev-Petviashvili instability [B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl...
Elastic instability in stratified core annular flow.
Bonhomme, Oriane; Morozov, Alexander; Leng, Jacques; Colin, Annie
2011-06-01
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic--it is caused by the viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation supplemented with a kinematic criterion captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure the rheological properties of dilute polymer solutions that are difficult to assess otherwise.
Elastic instability in stratified core annular flow
Bonhomme, Oriane; Leng, Jacques; Colin, Annie
2010-01-01
We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.
Kato, Takehisa; Yoshida, Ryuji; Yamamoto, Kazuo; Hirayama, Tsukasa; Motoyama, Munekazu; West, William C.; Iriyama, Yasutoshi
2016-09-01
Sintering processes yield a mutual diffusion region at the electrode/solid electrolyte interface, which is considered as a crucial problem for developing large-sized all-solid-state rechargeable lithium batteries with high power density. This work focuses on the interface between LiNi1/3Co1/3Mn1/3O2 (NMC) and NASICON-structured Li+ conductive glass ceramics solid electrolyte (Li2Osbnd Al2O3sbnd SiO2sbnd P2O5sbnd TiO2sbnd GeO2: LATP sheet (AG-01)), and investigates the effects of sintering temperature on interfacial structure and interfacial resistance at the NMC/LATP sheet. Thin films of NMC were fabricated on the LATP sheets at 700 °C or 900 °C as a model system. We found that the thickness of the mutual diffusion region was almost the same, ca. 30 nm, in these two samples, but the NMC film prepared at 900 °C had three orders of magnitude larger interfacial resistance than the NMC film prepared at 700 °C. Around the interface between the NMC film prepared at 900 °C and the LATP sheet, Co in the NMC accumulates as a reduced valence and lithium-free impurity crystalline phase will be also formed. These two problems must contribute to drastic increasing of interfacial resistance. Formation of de-lithiated NMC around the interface and its thermal instability at higher temperature may be considerable reason to induce these problems.
Interfacial transport processes and rheology
Brenner, Howard
1991-01-01
This textbook is designed to provide the theory, methods of measurement, and principal applications of the expanding field of interfacial hydrodynamics. It is intended to serve the research needs of both academic and industrial scientists, including chemical or mechanical engineers, material and surface scientists, physical chemists, chemical and biophysicists, rheologists, physiochemical hydrodynamicists, and applied mathematicians (especially those with interests in viscous fluid mechanics and continuum mechanics).As a textbook it provides materials for a one- or two-semester graduate-level
Electron heat flux instability
Saeed, Sundas; Sarfraz, M.; Yoon, P. H.; Lazar, M.; Qureshi, M. N. S.
2017-02-01
The heat flux instability is an electromagnetic mode excited by a relative drift between the protons and two-component core-halo electrons. The most prominent application may be in association with the solar wind where drifting electron velocity distributions are observed. The heat flux instability is somewhat analogous to the electrostatic Buneman or ion-acoustic instability driven by the net drift between the protons and bulk electrons, except that the heat flux instability operates in magnetized plasmas and possesses transverse electromagnetic polarization. The heat flux instability is also distinct from the electrostatic counterpart in that it requires two electron species with relative drifts with each other. In the literature, the heat flux instability is often called the 'whistler' heat flux instability, but it is actually polarized in the opposite sense to the whistler wave. This paper elucidates all of these fundamental plasma physical properties associated with the heat flux instability starting from a simple model, and gradually building up more complexity towards a solar wind-like distribution functions. It is found that the essential properties of the instability are already present in the cold counter-streaming electron model, and that the instability is absent if the protons are ignored. These instability characteristics are highly reminiscent of the electron firehose instability driven by excessive parallel temperature anisotropy, propagating in parallel direction with respect to the ambient magnetic field, except that the free energy source for the heat flux instability resides in the effective parallel pressure provided by the counter-streaming electrons.
Evaluating shoulder instability treatment
van der Linde, J.A.
2016-01-01
Shoulder instability common occurs. When treated nonoperatively, the resulting societal costs based on health care utilization and productivity losses are significant. Shoulder function can be evaluated using patient reported outcome measurements (PROMs). For shoulder instability, these include the
Jeans instability in superfluids
Energy Technology Data Exchange (ETDEWEB)
Hason, Itamar; Oz, Yaron [Tel-Aviv University, Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv (Israel)
2014-11-15
We analyze the effect of a gravitational field on the sound modes of superfluids. We derive an instability condition that generalizes the well-known Jeans instability of the sound mode in normal fluids. We discuss potential experimental implications. (orig.)
Double Rosensweig instability in a ferrofluid sandwich structure
Rannacher, Dirk; Engel, Andreas
2003-01-01
We consider a horizontal ferrofluid layer sandwiched between two layers of immiscible non-magnetic fluids. In a sufficiently strong vertical magnetic field the flat interfaces between magnetic and non-magnetic fluids become unstable to the formation of peaks. We theoretically investigate the interplay between these two instabilities for different combinations of the parameters of the fluids and analyze the evolving interfacial patterns. We also estimate the critical magnetic field strength at...
Gravitational instabilities in astrophysical fluids
Tohline, Joel E.
1990-01-01
Over the past decade, the significant advancements that have been made in the development of computational tools and numerical techniques have allowed astrophysicists to begin to model accurately the nonlinear growth of gravitational instabilities in a variety of physical systems. The fragmentation or rotationally driven fission of dynamically evolving, self-gravitating ``drops and bubbles'' is now routinely modeled in full three-dimensional generality as we attempt to understand the behavior of protostellar clouds, rotating stars, galaxies, and even the primordial soup that defined the birth of the universe. A brief review is presented here of the general insights that have been gained from studies of this type, followed by a somewhat more detailed description of work, currently underway, that is designed to explain the process of binary star formation. A short video animation sequence, developed in conjunction with some of the research being reviewed, illustrates the basic-nature of the fission instability in rotating stars and of an instability that can arise in a massive disk that forms in a protostellar cloud.
THREE-BEAM INSTABILITY IN THE LHC*
Burov, A
2013-01-01
In the LHC, a transverse instability is regularly observed at 4TeV right after the beta-squeeze, when the beams are separated by about their ten transverse rms sizes [1-3], and only one of the two beams is seen as oscillating. So far only a single hypothesis is consistent with all the observations and basic concepts, one about a third beam - an electron cloud, generated by the two proton beams in the high-beta areas of the interaction regions. The instability results from a combined action of the cloud nonlinear focusing and impedance.
Efficiency Versus Instability in Plasma Accelerators
Energy Technology Data Exchange (ETDEWEB)
Lebedev, Valeri [Fermilab; Burov, Alexey [Fermilab; Nagaitsev, Sergei [Fermilab
2017-01-05
Plasma wake-field acceleration in a strongly nonlinear (a.k.a. the blowout) regime is one of the main candidates for future high-energy colliders. For this case, we derive a universal efficiency-instability relation, between the power efficiency and the key instability parameter of the witness bunch. We also show that in order to stabilize the witness bunch in a regime with high power efficiency, the bunch needs to have high energy spread, which is not presently compatible with collider-quality beam properties. It is unclear how such limitations could be overcome for high-luminosity linear colliders.
Methods for Simulating the Heavy Core Instability
Directory of Open Access Journals (Sweden)
Chang Philip
2013-04-01
Full Text Available Vortices have been proposed as the sites of planet formation, where dust collects and grows into planetesimals, the building blocks of planets. However, for very small dust particles that can be treated as a pressure-less fluid, we have recently discovered the “heavy core” instability, driven by the density gradient in the vortex. In order to understand the eventual outcome of this instability, we need to study its non-linear development. Here, we describe our ongoing work to develop highly accurate numerical models of a vortex with a density gradient embedded within a protoplanetary disk.
Secondary instability of wall-bounded shear flows
Orszag, S. A.; Patera, A. T.
1983-01-01
The present analysis of a secondary instability in a wide class of wall-bounded parallel shear flows indicates that two-dimensional, finite amplitude waves are exponentially unstable to infinitessimal three-dimensional disturbances. The instability appears to be the prototype of transitional instability in such flows as Poiseuille flow, Couette flow, and flat plate boundary layers, in that it has the convective time scales observed in the typical transitions. The energetics and vorticity dynamics of the instability are discussed, and it is shown that the two-dimensional perturbation without directly providing energy to the disturbance. The three-dimensional instability requires that a threshold two-dimensional amplitude be achieved. It is found possible to identify experimental features of transitional spot structure with aspects of the nonlinear two-dimensional/linear three-dimensional instability.
Simulation and quasilinear theory of aperiodic ordinary mode instability
Energy Technology Data Exchange (ETDEWEB)
Seough, Jungjoon [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan); International Research Fellow of the Japan Society for the Promotion of Science, Tokyo (Japan); Yoon, Peter H. [Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of); Hwang, Junga [Korea Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Department of Astronomy and Space Science, University of Science and Technology, Daejeon (Korea, Republic of); Nariyuki, Yasuhiro [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan)
2015-08-15
The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy for high-beta plasmas was first discovered in the 1970s. This instability receives renewed attention because it may be applicable to the solar wind plasma. The electrons in the solar wind feature temperature anisotropies whose upper values are apparently limited by plasma instabilities. The O-mode instability may be important in this regard. Previous studies of O mode instability have been based on linear theory, but the actual solar wind electrons may be in saturated state. The present paper investigates the nonlinear saturation behavior of the O mode instability by means of one-dimensional particle-in-cell simulation and quasilinear theory. It is shown that the quasilinear method accurately reproduces the simulation results.
Interfacial reactions between titanium and borate glass
Energy Technology Data Exchange (ETDEWEB)
Brow, R.K. [Sandia National Labs., Albuquerque, NM (United States); Saha, S.K.; Goldstein, J.I. [Lehigh Univ., Bethlehem, PA (United States). Dept. of Materials Science
1992-12-31
Interfacial reactions between melts of several borate glasses and titanium have been investigated by analytical scanning electron microscopy (SEM) and x-ray photoelectron spectroscopy (XPS). A thin titanium boride interfacial layer is detected by XPS after short (30 minutes) thermal treatments. ASEM analyses after longer thermal treatments (8--120 hours) reveal boron-rich interfacial layers and boride precipitates in the Ti side of the interface.
Interfacial capacitance effects in magnetic tunneling junctions
Landry, G; Du, J; Xiao, J Q
2001-01-01
We have investigated the AC transport properties of magnetic tunnel junctions (MTJ) in order to characterize interfacial properties. One such property is interfacial charge accumulation, which leads to a voltage drop in the electrodes of the MTJ and the measured capacitance differing from the geometrical capacitance. Through measurement of capacitance spectra, we have extracted an interfacial capacitance of 16 mu F/cm sup 2 per interface and a screening length of 0.55 A for FeNi electrodes.
The Abelianization of QCD Plasma Instabilities
Arnold, P; Arnold, Peter; Lenaghan, Jonathan
2004-01-01
QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities i...
Relativistic Gravothermal Instabilities
Roupas, Zacharias
2014-01-01
The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the case of static, spherically symmetric configurations in General Relativity taking into account the Tolman-Ehrenfest effect. One type of instabilities is found at low energies, where thermal energy becomes too weak to halt gravity and another at high energies, where gravitational attraction of thermal pressure overcomes its stabilizing effect. These turning points of stability are found to depend on the total rest mass $\\mathcal{M}$ over the radius $R$. The low energy instability is the relativistic generalization of Antonov instability, which is recovered in the limit $G\\mathcal{M} \\ll R c^2$ and low temperatures, while in the same limit and high temperatures, the high energy instability recovers the instability of the radiation equation of state. In the temperature versus energy diagram of series of equilibria, the two types of gravothermal instabilities make themselves evident as a double spiral! The two energy l...
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Instability saturation by the oscillating two-stream instability in a weakly relativistic plasma
Energy Technology Data Exchange (ETDEWEB)
Pal, Barnali; Poria, Swarup, E-mail: swarup-p@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India)
2015-04-15
The two-stream instability has wide range of astrophysical applications starting from gamma-ray bursts and pulsar glitches to cosmology. We consider one dimensional weakly relativistic Zakharov equations and describe nonlinear saturation of the oscillating two-stream instability using a three dimensional dynamical system resulting form a truncation of the nonlinear Schrodinger equation to three modes. The equilibrium points of the model are determined and their stability natures are discussed. Using the tools of nonlinear dynamics such as the bifurcation diagram, Poincaré maps, and Lyapunav exponents, existence of periodic, quasi-periodic, and chaotic solutions are established in the dynamical system. Interestingly, we observe the multistable behavior in this plasma model. The system has multiple attractors depending on the initial conditions. We also notice that the relativistic parameter plays the role of control parameter in the model. The theoretical results presented in this paper may be helpful for better understanding of space and astrophysical plasmas.
2016-12-13
their mitigation with applications in scaling of pulsed and continuous- wave high- energy lasers Balaji Srinivasan INDIAN INSTITUTE OF TECHNOLOGY...high- energy lasers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-15-1-5044 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S) Balaji Srinivasan 5d...use of vortex beams to mitigate thermal mode instability in high energy fiber amplifiers. The investigation is carried out through (1) the
Explosive Instability of Prominence Flux Ropes
Energy Technology Data Exchange (ETDEWEB)
Hurricane, O; Fong, R H L; Cowley, S C
2002-09-04
The rapid, Alfvenic, time scale of erupting solar-prominences has been an enigma ever since they where first identified. Investigators have proposed a variety of different mechanisms in an effort to account for the abrupt reconfiguration observed. No one mechanism clearly stands out as the single cause of these explosive events. Recent analysis has demonstrated that field lines in the solar atmosphere are metastable to ballooning type instabilities. It has been found previously that in ideal MHD plasmas marginally unstable ballooning modes inevitably become ''explosive'' evolving towards a finite time singularity via a nonlinear 3D instability called ''Nonlinear Magnetohydrodynamic Detonation.'' Thus, this mechanism is a good candidate to explain explosive events observed in the solar atmosphere of our star or in others.
Fluctuations and correlations in modulation instability
Solli, D. R.; Herink, G.; Jalali, B.; Ropers, C.
2012-07-01
Stochastically driven nonlinear processes are responsible for spontaneous pattern formation and instabilities in numerous natural and artificial systems, including well-known examples such as sand ripples, cloud formations, water waves, animal pigmentation and heart rhythms. Technologically, a type of such self-amplification drives free-electron lasers and optical supercontinuum sources whose radiation qualities, however, suffer from the stochastic origins. Through time-resolved observations, we identify intrinsic properties of these fluctuations that are hidden in ensemble measurements. We acquire single-shot spectra of modulation instability produced by laser pulses in glass fibre at megahertz real-time capture rates. The temporally confined nature of the gain physically limits the number of amplified modes, which form an antibunched arrangement as identified from a statistical analysis of the data. These dynamics provide an example of pattern competition and interaction in confined nonlinear systems.
Baroclinic Instability on Hot Extrasolar Planets
Polichtchouk, Inna
2012-01-01
We investigate baroclinic instability in flow conditions relevant to hot extrasolar planets. The instability is important for transporting and mixing heat, as well as for influencing large-scale variability on the planets. Both linear normal mode analysis and non-linear initial value calculations are carried out -- focusing on the freely-evolving, adiabatic situation. Using a high-resolution general circulation model (GCM) which solves the traditional primitive equations, we show that large-scale jets similar to those observed in current GCM simulations of hot extrasolar giant planets are likely to be baroclinically unstable on a timescale of few to few tens of planetary rotations, generating cyclones and anticyclones that drive weather systems. The growth rate and scale of the most unstable mode obtained in the linear analysis are in qualitative, good agreement with the full non-linear calculations. In general, unstable jets evolve differently depending on their signs (eastward or westward), due to the chang...
Protein interfacial structure and nanotoxicology
Energy Technology Data Exchange (ETDEWEB)
White, John W. [Research School of Chemistry, Australian National University, Canberra (Australia)], E-mail: jww@rsc.anu.edu.au; Perriman, Adam W.; McGillivray, Duncan J.; Lin, J.-M. [Research School of Chemistry, Australian National University, Canberra (Australia)
2009-02-21
Here we briefly recapitulate the use of X-ray and neutron reflectometry at the air-water interface to find protein structures and thermodynamics at interfaces and test a possibility for understanding those interactions between nanoparticles and proteins which lead to nanoparticle toxicology through entry into living cells. Stable monomolecular protein films have been made at the air-water interface and, with a specially designed vessel, the substrate changed from that which the air-water interfacial film was deposited. This procedure allows interactions, both chemical and physical, between introduced species and the monomolecular film to be studied by reflectometry. The method is briefly illustrated here with some new results on protein-protein interaction between {beta}-casein and {kappa}-casein at the air-water interface using X-rays. These two proteins are an essential component of the structure of milk. In the experiments reported, specific and directional interactions appear to cause different interfacial structures if first, a {beta}-casein monolayer is attacked by a {kappa}-casein solution compared to the reverse. The additional contrast associated with neutrons will be an advantage here. We then show the first results of experiments on the interaction of a {beta}-casein monolayer with a nanoparticle titanium oxide sol, foreshadowing the study of the nanoparticle 'corona' thought to be important for nanoparticle-cell wall penetration.
Interfacial coarsening dynamics in epitaxial growth with slope selection
Moldovan; Golubovic
2000-06-01
We investigate interfacial dynamics of molecular-beam epitaxy (MBE) growth in the presence of instabilities inducing formation of pyramids. We introduce a kinetic scaling theory which provides an analytic understanding of the coarsening dynamics laws observed in numerous experiments and simulations of the MBE. We address MBE growth on crystalline surfaces with different symmetries in order to explain experimentally observed differences between the growth on (111) and (001) surfaces and understand the coarsening exponents measured on these surfaces. We supplement our kinetic scaling theory by numerical simulations which document that the edges of the pyramids, forming a network across the growing interface, are essential for qualitative understanding of the coarsening dynamics of molecular-beam epitaxy.
Magnetic interchange instability of accretion disks
Kaisig, M.; Tajima, T.; Lovelace, R. V. E.
1992-01-01
The nonlinear evolution of the magnetic interchange or buoyancy instability of a differentially rotating disk threaded by an ordered vertical magnetic field is investigated. A 2D ideal fluid in the equatorial plane of a central mass in the corotating frame of reference is considered as a model for the disk. If the rotation rate of the disk is Keplerian, the disk is found to be stable. If the vertical magnetic field is sufficiently strong, and the field strength decreases with distance from the central object, and thus the rotation of the disk deviates from Keplerian, if is found that an instability develops. The magnetic flux and disk matter expand outward in certain ranges of azimuth, while disk matter with less magnetic flux moves inward over the remaining range of azimuth, showing a characteristic development of an interchange instability.
Shoulder instability; Schulterinstabilitaeten
Energy Technology Data Exchange (ETDEWEB)
Kreitner, Karl-Friedrich [Mainiz Univ. (Germany). Klinik und Poliklinik fuer Diagnostische und Interventionelle Radiologie
2014-06-15
In the shoulder, the advantages of range of motion are traded for the disadvantages of vulnerability to injury and the development of instability. Shoulder instability and the lesion it produces represent one of the main causes of shoulder discomfort and pain. Shoulder instability is defined as a symptomatic abnormal motion of the humeral head relative to the glenoid during active shoulder motion. Glenohumeral instabilities are classified according to their causative factors as the pathogenesis of instability plays an important role with respect to treatment options: instabilities are classified in traumatic and atraumatic instabilities as part of a multidirectional instability syndrome, and in microtraumatic instabilities. Plain radiographs ('trauma series') are performed to document shoulder dislocation and its successful reposition. Direct MR arthrography is the most important imaging modality for delineation the different injury patterns on the labral-ligamentous complex and bony structures. Monocontrast CT-arthrography with use of multidetector CT scanners may be an alternative imaging modality, however, regarding the younger patient age, MR imaging should be preferred in the diagnostic work-up of shoulder instabilities. (orig.)
Laser driven hydrodynamic instability experiments. Revision 1
Energy Technology Data Exchange (ETDEWEB)
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.
1993-02-17
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.
Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.
2016-05-01
An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.
Quasilinear saturation of the aperiodic ordinary mode streaming instability
Energy Technology Data Exchange (ETDEWEB)
Stockem Novo, A., E-mail: anne@tp4.rub.de; Schlickeiser, R. [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum-und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Yoon, P. H. [Institute for Physical Science & Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of); Lazar, M. [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum-und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Poedts, S. [Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Seough, J. [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan); International Research Fellow of the Japan Society for the Promotion of Science, Tokyo (Japan)
2015-09-15
In collisionless plasmas, only kinetic instabilities and fluctuations are effective in reducing the free energy and scatter plasma particles, preventing an increase of their anisotropy. Solar energetic outflows into the interplanetary plasma give rise to important thermal anisotropies and counterstreaming motions of plasma shells, and the resulting instabilities are expected to regulate the expansion of the solar wind. The present paper combines quasilinear theory and kinetic particle-in-cell simulations in order to study the weakly nonlinear saturation of the ordinary mode in hot counter-streaming plasmas with a temperature anisotropy as a follow-up of the paper by Seough et al. [Phys. Plasmas 22, 082122 (2015)]. This instability provides a plausible mechanism for the origin of dominating, two-dimensional spectrum of transverse magnetic fluctuations observed in the solar wind. Stimulated by the differential motion of electron counterstreams the O mode instability may convert their free large-scale energy by nonlinear collisionless dissipation on plasma particles.
Dynamic properties of combustion instability in a lean premixed gas-turbine combustor.
Gotoda, Hiroshi; Nikimoto, Hiroyuki; Miyano, Takaya; Tachibana, Shigeru
2011-03-01
We experimentally investigate the dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor from the viewpoint of nonlinear dynamics. A nonlinear time series analysis in combination with a surrogate data method clearly reveals that as the equivalence ratio increases, the dynamic behavior of the combustion instability undergoes a significant transition from stochastic fluctuation to periodic oscillation through low-dimensional chaotic oscillation. We also show that a nonlinear forecasting method is useful for predicting the short-term dynamic behavior of the combustion instability in a lean premixed gas-turbine combustor, which has not been addressed in the fields of combustion science and physics.
Analytical analysis of modulation instability in fiber optics
Directory of Open Access Journals (Sweden)
M. Saeed Aslam
2012-06-01
Full Text Available In this paper, an improved analysis for modulation instability, which results from interaction between optical wave and noise, is presented. It is shown that Nonlinear Schrodinger equation (NLSE, which governs this process, leads to the coupled wave equations that result to Riccati's differential equations. A completely analytical solution of Riccati's equation is obtained for small fiber length that results in efficient computation of the modulation instability effect.
Model of e-cloud instability in the Fermilab Recycler
Balbekov, V
2015-01-01
Simple model of electron cloud is developed in the paper to explain e-cloud instability of bunched proton beam in the Fermilab Recycler. The cloud is presented as an immobile snake in strong vertical magnetic field. The instability is treated as an amplification of the bunch injection errors from the batch head to its tail. Nonlinearity of the e-cloud field is taken into account. Results of calculations are compared with experimental data demonstrating good correlation.
Model of E-Cloud Instability in the Fermilab Recycler
Energy Technology Data Exchange (ETDEWEB)
Balbekov, V. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2015-06-24
Simple model of electron cloud is developed in the paper to explain e-cloud instability of bunched proton beam in the Fermilab Recycler. The cloud is presented as an immobile snake in strong vertical magnetic field. The instability is treated as an amplification of the bunch injection errors from the batch head to its tail. Nonlinearity of the e-cloud field is taken into account. Results of calculations are compared with experimental data demonstrating good correlation.
Analysis of Kelvin Helmholtz Instabilities of Plasma Jets
Friedman, Mark J.; Hollingsworth, Blane J.
1999-01-01
Ulysses data indicates density fluctuations which are theorized to be the result of shear between a solar jet and its ambient. The MHD Kelvin-Helmholtz ("KH") instability causes such fluctuations as observed by Ulysses. A new dispersion relationship which accounts for this KH instability is derived via the linearization of the MHD equations. This generalizes an earlier result by Hardee. This dispersion relationship has the form of eight non-linear equations with nine unknowns.
Xiao, Minyu; Joglekar, Suneel; Zhang, Xiaoxian; Jasensky, Joshua; Ma, Jialiu; Cui, Qingyu; Guo, L Jay; Chen, Zhan
2017-03-08
A wide variety of charge carrier dynamics, such as transport, separation, and extraction, occur at the interfaces of planar heterojunction solar cells. Such factors can affect the overall device performance. Therefore, understanding the buried interfacial molecular structure in various devices and the correlation between interfacial structure and function has become increasingly important. Current characterization techniques for thin films such as X-ray diffraction, cross section scanning electronmicroscopy, and UV-visible absorption spectroscopy are unable to provide the needed molecular structural information at buried interfaces. In this study, by controlling the structure of the hole transport layer (HTL) in a perovskite solar cell and applying a surface/interface-sensitive nonlinear vibrational spectroscopic technique (sum frequency generation vibrational spectroscopy (SFG)), we successfully probed the molecular structure at the buried interface and correlated its structural characteristics to solar cell performance. Here, an edge-on (normal to the interface) polythiophene (PT) interfacial molecular orientation at the buried perovskite (photoactive layer)/PT (HTL) interface showed more than two times the power conversion efficiency (PCE) of a lying down (tangential) PT interfacial orientation. The difference in interfacial molecular structure was achieved by altering the alkyl side chain length of the PT derivatives, where PT with a shorter alkyl side chain showed an edge-on interfacial orientation with a higher PCE than that of PT with a longer alkyl side chain. With similar band gap alignment and bulk structure within the PT layer, it is believed that the interfacial molecular structural variation (i.e., the orientation difference) of the various PT derivatives is the underlying cause of the difference in perovskite solar cell PCE.
Hydrodynamic Instabilities in Rotating Fluids
Institute of Scientific and Technical Information of China (English)
KarlBuehler
2000-01-01
Rotating flow systems are often used to study stability phenomena and structure developments.The closed spherical gap prblem is generalized into an open flow system by superimposing a mass flux in meridional direction.The basic solutions at low Reynolds numbers are described by analytical methods.The nonlinear supercritical solutions are simulated numerically and realized in experiments.Novel steady and time-dependent modes of flows are obtained.The extensive results concern the stability behaviour.non-uniqueness of supercritical solutions,symmetry behaviour and transitions between steady and time-dependent solutions.The experimental investigations concern the visualization of the various instabilities and the quatitative description of the flow structures including the laminar-turbulent transition.A Comparison between theoretical and experimental results shows good agreement within the limit of rotational symmetric solutions from the theory.
Competition between Buneman and Langmuir Instabilities
Institute of Scientific and Technical Information of China (English)
GUO Jun; YU Bin
2012-01-01
The electron-ion beam instabilities are studied by one-dimensional electrostatic particle-in-cell simulation.The simulation results show that both the low-frequency Buneman mode and high-frequency Langmuir wave (LW) are excited in the nonlinear phase. The power of Buneman instability is stronger than that of the LW.The Buneman instability is firstly excited.Then the backward LW appears,which is probably excited by the particles trapped in the wave potential and moving opposite to the original beam direction.After some time,the forward LW can be found,which has a larger maximum frequency than that of the backward LW.With the decrease of the electron drift velocity,the instabilities become weaker; the LW appears to have almost equal intensities and becomes symmetric for forward and backward propagation directions. The LW can also heat the electron,so the relative drift speed cannot far exceed the electron thermal speed,which is not helpful to the development of Buneman instability.
Paul, Shirshendu; Katiyar, Amit; Sarkar, Kausik; Chatterjee, Dhiman; Shi, William T; Forsberg, Flemming
2010-06-01
Two nonlinear interfacial elasticity models--interfacial elasticity decreasing linearly and exponentially with area fraction--are developed for the encapsulation of contrast microbubbles. The strain softening (decreasing elasticity) results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties (surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters) for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension (the encapsulation experiences no net compressive stress) shows "compression-only" behavior. The exponential and the quadratic (linearly varying elasticity) models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation.
Dynamic Instability of Rapidly Rotating Protostars
Pickett, B. K.; Durisen, R. H.; Johnson, M. S.; Davis, G. A.
1994-12-01
Modern studies of collapse and fragmentation of protostellar clouds suggest a wide variety of outcomes, depending on the assumed initial conditions. Individual equilibrium objects which result from collapse are likely to be in rapid rotation and can have a wide range of structures. We have undertaken a survey of parameter space in order to examine the role of dynamic instabilities in the subsequent evolution of these objects. For the purposes of conducting a systematic study, we so far have considered only the n = 3/2 polytropic equilibrium states that might form from the collapse of uniformly rotating spherical clouds. By varying the central concentration of the assumed initial cloud, we obtain equilibrium states distinguished primarily by their different specific angular momentum distributions. These equilibrium states span the range between starlike objects with angular momentum distributions analogous to the Maclaurin spheroids and objects more accurately described as massive Keplerian disks around stars. Using a new SCF code to generate the n = 3/2 axisymmetric equilibrium states and an improved 3D hydrodynamics code, we have investigated the the onset and nature of global dynamic instabilities in these objects. The starlike objects are unstable to barlike instabilities at T/|W| gtorder 0.27, where T/|W| is the ratio of total rotational kinetic energy to gravitational potential energy. These instabilities are vigorous and lead to violent ejection of mass and angular momentum. As the angular momentum distribution shifts to the other extreme, one- and two-armed spiral instabilities begin to dominate at considerably lower T/|W|. These instabilities appear to be driven by the SLING and swing mechanisms. In extremely flattened disks, one-armed spirals dominate all other disturbances but eventually saturate at nonlinear amplitude without producing fragmentation. We conclude that the nature of the global instabilities encountered during the process of star formation
Suppression of electromechanical instability in fiber-reinforced dielectric elastomers
Directory of Open Access Journals (Sweden)
Rui Xiao
2016-03-01
Full Text Available The electromechanical instability of dielectric elastomers has been a major challenge for the application of this class of active materials. In this work, we demonstrate that dielectric elastomers filled with soft fiber can suppress the electromechanical instability and achieve large deformation. Specifically, we developed a constitutive model to describe the dielectric and mechanical behaviors of fiber-reinforced elastomers. The model was applied to study the influence of stiffness, nonlinearity properties and the distribution of fiber on the instability of dielectric membrane under an electric field. The results show that there exists an optimal fiber distribution condition to achieve the maximum deformation before failure.
Reactive-infiltration instabilities in rocks. Fracture dissolution
Szymczak, Piotr
2012-01-01
A reactive fluid dissolving the surface of a uniform fracture will trigger an instability in the dissolution front, leading to spontaneous formation of pronounced well-spaced channels in the surrounding rock matrix. Although the underlying mechanism is similar to the wormhole instability in porous rocks there are significant differences in the physics, due to the absence of a steadily propagating reaction front. In previous work we have described the geophysical implications of this instability in regard to the formation of long conduits in soluble rocks. Here we describe a more general linear stability analysis, including axial diffusion, transport limited dissolution, non-linear kinetics, and a finite length system.
Observation of coherent instability in the CERN PS Booster
McAteer, M; Forte, V; Rumolo, G; Tomás, R
2014-01-01
At high intensities and at certain working points, an instability develops in the CERN PS Booster and large coherent transverse oscillations and beam loss occur [1]. The coherent oscillations and beam loss can be effectively controlled with the transverse damper system, but the origin of the instability is not well understood. In preparation for nonlinear optics measurements in the PS Booster that will take place after CERN’s first Long Shutdown, trial measurements were made with the PSB’s new trajectory measurement system. The measurements gave some new insight into the nature of this transverse instability, and these observations are presented here.
Kinetic effects in the transverse filamentation instability of pair plasmas
Directory of Open Access Journals (Sweden)
D'Angelo M.
2015-01-01
Full Text Available The evolution of the filamentation instability produced by two counter-streaming pair plasmas is studied with particle-in-cell (PIC simulations in both one (1D and two (2D spatial dimensions. Radiation friction effects on particles are taken into account. During the nonlinear stage of the instability, a strong broadening of the particle energy spectrum occurs accompanied by the formation of a peak at twice their initial energy. A simple theory of the peak formation is presented. The presence of radiative losses does not change the dynamics of the instability but affects the structure of the particle spectra.
Electrokinetic Instability near Charge-Selective Hydrophobic Surfaces
Shelistov, V S; Ganchenko, G S
2014-01-01
The influence of the texture of a hydrophobic surface on the electro-osmotic slip of the second kind and the electrokinetic instability near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a simple model based on the Rubinstein-Zaltzman approach. A simple formula is derived to evaluate the decrease in the instability threshold due to hydrophobicity. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a hydrophobic membrane surface. Theory predicts a significant enhancement of the ion flux to the surface and shows a good qualitative agreement with the available experimental data.
On the transition between the Weibel and the whistler instabilities
Palodhi, L; Pegoraro, F; 10.1088/0741-3335/52/9/09500
2010-01-01
The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial modulation of the amplitude of the magnetic field generated by the whistler instability.
Linear inner cladding fiber amplifier suppressing mode instability
Li, Zebiao; Huang, Zhihua; Lin, Honghuan; Xu, Shanhui; Yang, Zhongmin; Wang, Jianjun; Jing, Feng
2016-11-01
We use a semi-analytical model considering pump power saturation in high power fiber laser systems of multi-kW-class to calculate mode instability threshold. A novel designed fiber, linear inner-cladding fiber, can mitigate mode instability effect by decreasing nonlinear coupling coefficient and smoothing heat profile along the fiber. We investigate strong pump absorption of linear inner-cladding fiber, leading to shorter fiber length. With 915 nm pumping, linear inner-cladding fiber can reach 10 kW output power without mode instability in theory.
Buoyancy Instabilities in a Weakly Collisional Intracluster Medium
Kunz, Matthew W; Reynolds, Christopher S; Stone, James M
2012-01-01
The intracluster medium of galaxy clusters is a weakly collisional, high-beta plasma in which the transport of heat and momentum occurs primarily along magnetic-field lines. Anisotropic heat conduction allows convective instabilities to be driven by temperature gradients of either sign, the magnetothermal instability (MTI) in the outskirts of non-isothermal clusters and the heat-flux buoyancy-driven instability (HBI) in their cooling cores. We employ the Athena MHD code to investigate the nonlinear evolution of these instabilities, self-consistently including the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy), anisotropic conduction, and radiative cooling. We highlight the importance of the microscale instabilities that inevitably accompany and regulate the pressure anisotropies generated by the HBI and MTI. We find that, in all but the innermost regions of cool-core clusters, anisotropic viscosity significantly impairs the ability of the HBI to reorient magnetic-field lines orthogonal...
Rayleigh-Taylor instability in accelerated solid media
Piriz, A. R.; Sun, Y. B.; Tahir, N. A.
2017-01-01
A linear study of the Rayleigh-Taylor instability based on momentum conservation and the consideration of an irrotational velocity field for incompressible perturbations is discussed. The theory allows for a very appealing physical picture and for a relatively simple description of the main features of the instability. As a result, it is suitable for the study of the very complex problem of the instability of accelerated solids with non-linear elastic-plastic constitutive properties, which cannot be studied by the usual normal modes approach. The elastic to plastic transition occurring early in the instability process determines the entire evolution and makes the instability exhibit behavior that cannot be captured by an asymptotic analysis.
Coupling of transit time instabilities in electrostatic confinement fusion devices
Gruenwald, J.; Fröhlich, M.
2015-07-01
A model of the behavior of transit time instabilities in an electrostatic confinement fusion reactor is presented in this letter. It is demonstrated that different modes are excited within the spherical cathode of a Farnsworth fusor. Each of these modes is dependent on the fusion products as well as the acceleration voltage applied between the two electrodes and they couple to a resulting oscillation showing non-linear beat phenomena. This type of instability is similar to the transit time instability of electrons between two resonant surfaces but the presence of ions and the occurring fusion reactions alter the physics of this instability considerably. The physics of this plasma instability is examined in detail for typical physical parameter ranges of electrostatic confinement fusion devices.
Cavitation Instabilities in Inducers
2006-11-01
gas handling turbomachines . The fluctuation of the cavity length is plotted in Fig.8 under the surge mode oscillation vi . The major differences...Cavitation Instabilities of Turbomachines .” AIAA Journal of Propulsion and Power, Vol.17, No.3, 636-643. [5] Tsujimoto, Y., (2006), “Flow Instabilities in
Instability in evolutionary games.
Directory of Open Access Journals (Sweden)
Zimo Yang
Full Text Available BACKGROUND: Phenomena of instability are widely observed in many dissimilar systems, with punctuated equilibrium in biological evolution and economic crises being noticeable examples. Recent studies suggested that such instabilities, quantified by the abrupt changes of the composition of individuals, could result within the framework of a collection of individuals interacting through the prisoner's dilemma and incorporating three mechanisms: (i imitation and mutation, (ii preferred selection on successful individuals, and (iii networking effects. METHODOLOGY/PRINCIPAL FINDINGS: We study the importance of each mechanism using simplified models. The models are studied numerically and analytically via rate equations and mean-field approximation. It is shown that imitation and mutation alone can lead to the instability on the number of cooperators, and preferred selection modifies the instability in an asymmetric way. The co-evolution of network topology and game dynamics is not necessary to the occurrence of instability and the network topology is found to have almost no impact on instability if new links are added in a global manner. The results are valid in both the contexts of the snowdrift game and prisoner's dilemma. CONCLUSIONS/SIGNIFICANCE: The imitation and mutation mechanism, which gives a heterogeneous rate of change in the system's composition, is the dominating reason of the instability on the number of cooperators. The effects of payoffs and network topology are relatively insignificant. Our work refines the understanding on the driving forces of system instability.
Robbins, G M; Masri, B A; Garbuz, D S; Greidanus, N; Duncan, C P
2001-10-01
Instability after total hip arthroplasty is a major source of patient morbidity, second only to aseptic loosening. Certain patient groups have been identified as having a greater risk of instability, including patients undergoing revision arthroplasty as early or late treatment for proximal femoral fractures.
Sivan, Y; Fibich, G; Ilan, B; Weinstein, M I
2008-10-01
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.
Instability of two-dimensional solitons and vortices in defocusing media
Kuznetsov, E. A.; Rasmussen, J. Juul
1995-05-01
In the framework of the three-dimensional nonlinear Schrödinger equation the instability of two-dimensional solitons and vortices is demonstrated. The soliton instability can be considered as the analog of the Kadomtsev-Petviashvili instability (Dokl. Akad. Nauk SSSR 192, 753 (1970) [Sov. Phys. Dokl. 15, 539 (1970)]) of one-dimensional acoustic solitons in media with positive dispersion. For large distances between the vortices, this instability transforms into the Crow instability [AIAA J. 8, 2172 (1970)] of two vortex filaments with opposite circulations.
Theoretical analysis of mode instability in high-power fiber amplifiers
DEFF Research Database (Denmark)
Hansen, Kristian Rymann; Alkeskjold, Thomas Tanggaard; Broeng, Jes;
2013-01-01
We present a simple theoretical model of transverse mode instability in high-power rare-earth doped fiber amplifiers. The model shows that efficient power transfer between the fundamental and higher-order modes of the fiber can be induced by a nonlinear interaction mediated through the thermo......-optic effect, leading to transverse mode instability. The temporal and spectral characteristics of the instability dynamics are investigated, and it is shown that the instability can be seeded by both quantum noise and signal intensity noise, while pure phase noise of the signal does not induce instability...
Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.
2016-12-01
Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Extended propagation model for interfacial crack in composite material structure
Institute of Scientific and Technical Information of China (English)
闫相桥; 冯希金
2002-01-01
An interfacial crack is a common damage in a composite material structure . An extended propaga-tion model has been established for an interfacial crack to study the dependence of crack growth on the relativesizes of energy release rates at left and right crack tips and the properties of interfacial material characterize thegrowth of interfacial crack better.
Interfacial closure of contacting surfaces
Rieutord, F.; Rauer, C.; Moriceau, H.
2014-08-01
Understanding the contact between solid surfaces is a long-standing problem which has a strong impact on the physics of many processes such as adhesion, friction, lubrication and wear. Experimentally, the investigation of solid/solid interfaces remains challenging today, due to the lack of experimental techniques able to provide sub-nanometer scale information on interfaces buried between millimeters of materials. Yet, a strong interest exists improving the modeling of contact mechanics of materials in order to adjust their interface properties (e.g., thermal transport, friction). We show here that the essential features of the residual gap between contacting surfaces can be measured using high energy X-ray synchrotron reflectivity. The presence of this nano-gap is general to the contact of solids. In some special case however, it can be removed when attractive forces take over repulsive contributions, depending on both height and wavelength of asperity distributions (roughness). A criterion for this instability is established in the standard case of van der Waals attractive forces and elastic asperity compression repulsive forces (Hertz model). This collapse instability is confirmed experimentally in the case of silicon direct bonding, using high-energy X-ray synchrotron reflectivity and adhesion energy measurements. The possibility to achieve fully closed interfaces at room temperature opens interesting perspectives to build stronger assemblies with smaller thermal budgets.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Interfacial depinning transitions in disordered media: revisiting an old puzzle
Moglia, Belén; Albano, Ezequiel V.; Villegas, Pablo; Muñoz, Miguel A.
2014-10-01
Interfaces advancing through random media represent a number of different problems in physics, biology and other disciplines. Here, we study the pinning/depinning transition of the prototypical non-equilibrium interfacial model, i.e. the Kardar-Parisi-Zhang equation, advancing in a disordered medium. We analyze separately the cases of positive and negative non-linearity coefficients, which are believed to exhibit qualitatively different behavior: the positive case shows a continuous transition that can be related to directed-percolation-depinning while in the negative case there is a discontinuous transition and faceted interfaces appear. Some studies have argued from different perspectives that both cases share the same universal behavior. Here, by using a number of computational and scaling techniques we shed light on this puzzling situation and conclude that the two cases are intrinsically different.
Interfacial gauge methods for incompressible fluid dynamics
Saye, Robert
2016-01-01
Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of “gauge freedom” to reduce the...
Modeling interfacial fracture in Sierra.
Energy Technology Data Exchange (ETDEWEB)
Brown, Arthur A.; Ohashi, Yuki; Lu, Wei-Yang; Nelson, Stacy A. C.; Foulk, James W.,; Reedy, Earl David,; Austin, Kevin N.; Margolis, Stephen B.
2013-09-01
This report summarizes computational efforts to model interfacial fracture using cohesive zone models in the SIERRA/SolidMechanics (SIERRA/SM) finite element code. Cohesive surface elements were used to model crack initiation and propagation along predefined paths. Mesh convergence was observed with SIERRA/SM for numerous geometries. As the funding for this project came from the Advanced Simulation and Computing Verification and Validation (ASC V&V) focus area, considerable effort was spent performing verification and validation. Code verification was performed to compare code predictions to analytical solutions for simple three-element simulations as well as a higher-fidelity simulation of a double-cantilever beam. Parameter identification was conducted with Dakota using experimental results on asymmetric double-cantilever beam (ADCB) and end-notched-flexure (ENF) experiments conducted under Campaign-6 funding. Discretization convergence studies were also performed with respect to mesh size and time step and an optimization study was completed for mode II delamination using the ENF geometry. Throughout this verification process, numerous SIERRA/SM bugs were found and reported, all of which have been fixed, leading to over a 10-fold increase in convergence rates. Finally, mixed-mode flexure experiments were performed for validation. One of the unexplained issues encountered was material property variability for ostensibly the same composite material. Since the variability is not fully understood, it is difficult to accurately assess uncertainty when performing predictions.
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
Effect of Atmospheric Ions on Interfacial Water
Directory of Open Access Journals (Sweden)
Chien-Chang Kurt Kung
2014-11-01
Full Text Available The effect of atmospheric positivity on the electrical properties of interfacial water was explored. Interfacial, or exclusion zone (EZ water was created in the standard way, next to a sheet of Nafion placed horizontally at the bottom of a water-filled chamber. Positive atmospheric ions were created from a high voltage source placed above the chamber. Electrical potential distribution in the interfacial water was measured using microelectrodes. We found that beyond a threshold, the positive ions diminished the magnitude of the negative electrical potential in the interfacial water, sometimes even turning it to positive. Additionally, positive ions produced by an air conditioner were observed to generate similar effects; i.e., the electrical potential shifted in the positive direction but returned to negative when the air conditioner stopped blowing. Sometimes, the effect of the positive ions from the air conditioner was strong enough to destroy the structure of interfacial water by turning the potential decidedly positive. Thus, positive air ions can compromise interfacial water negativity and may explain the known negative impact of positive ions on health.
Interfacial area transport in bubbly flow
Energy Technology Data Exchange (ETDEWEB)
Ishii, M.; Wu, Q.; Revankar, S.T. [Purdue Univ., West Lafayette, IN (United States)] [and others
1997-12-31
In order to close the two-fluid model for two-phase flow analyses, the interfacial area concentration needs to be modeled as a constitutive relation. In this study, the focus was on the investigation of the interfacial area concentration transport phenomena, both theoretically and experimentally. The interfacial area concentration transport equation for air-water bubbly up-flow in a vertical pipe was developed, and the models for the source and sink terms were provided. The necessary parameters for the experimental studies were identified, including the local time-averaged void fraction, interfacial area concentration, bubble interfacial velocity, liquid velocity and turbulent intensity. Experiments were performed with air-water mixture at atmospheric pressure. Double-sensor conductivity probe and hot-film probe were employed to measure the identified parameters. With these experimental data, the preliminary model evaluation was carried out for the simplest form of the developed interfacial area transport equation, i.e., the one-dimensional transport equation.
Xu, Jian-Jun
2017-01-01
This comprehensive work explores interfacial instability and pattern formation in dynamic systems away from the equilibrium state in solidification and crystal growth. Further, this significantly expanded 2nd edition introduces and reviews the progress made during the last two decades. In particular, it describes the most prominent pattern formation phenomena commonly observed in material processing and crystal growth in the framework of the previously established interfacial wave theory, including free dendritic growth from undercooled melt, cellular growth and eutectic growth in directional solidification, as well as viscous fingering in Hele-Shaw flow. It elucidates the key problems, systematically derives their mathematical solutions by pursuing a unified, asymptotic approach, and finally carefully examines these results by comparing them with the available experimental results. The asymptotic approach described here will be useful for the investigation of pattern formation phenomena occurring in a much b...
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Raoelison, R. N.; Sapanathan, T.; Padayodi, E.; Buiron, N.; Rachik, M.
2016-11-01
This paper investigates the complex interfacial kinematics and governing mechanisms during high speed impact conditions. A robust numerical modelling technique using Eulerian simulations are used to explain the material response of the interface subjected to a high strain rate collision during a magnetic pulse welding. The capability of this model is demonstrated using the predictions of interfacial kinematics and revealing the governing mechanical behaviours. Numerical predictions of wave formation resulted with the upward or downward jetting and complex interfacial mixing governed by wake and vortex instabilities corroborate the experimental observations. Moreover, the prediction of the material ejection during the simulation explains the experimentally observed deposited particles outside the welded region. Formations of internal cavities along the interface is also closely resemble the resulted confined heating at the vicinity of the interface appeared from those wake and vortex instabilities. These results are key features of this simulation that also explains the potential mechanisms in the defects formation at the interface. These results indicate that the Eulerian computation not only has the advantage of predicting the governing mechanisms, but also it offers a non-destructive approach to identify the interfacial defects in an impact welded joint.
Institute of Scientific and Technical Information of China (English)
倪蕾; 杨志良
2011-01-01
以HarrisSheet作为初始条件，使用数值模拟的方法，研究了二级磁岛不稳定重联的一些性质．在模拟中随着初始扰动的加入，HarrisSheet将演化到非线性阶段，形成更薄的有剪切速度的电流片，并伴有一级磁岛产生．当Lundquist数大于或等于10^5时，非均匀剪切速度的Sweet-Parker电流片开始不稳定，并有二级磁岛出现．不稳定Sweet—Parker电流片对应的临界长宽比为65．Lundquist数越大，演化形成的Sweet—Parker电流片越薄，更多的二级磁岛将出现，且沿电流片两边向外喷出%In this paper, numerical simulation results of nonlinear Plasmoid instabilities are presented. A two dimensional incompressible MHD code is used to calculate the results. The adaptive mesh refinement and MPI techniques are enable in this code. Harris sheets are used as the initial equilibrium conditions and small perturbations of the current density are applied to make the system unstable. Sequences of plasmoid instability processses for different Lundquist numbers have been studied. The Harris sheets will always evolve in to thinner Sweet-Parker current sheets with shearing flows in the early stage. As the Lundquist number S 〉/10^5, the Sweet-Parker thin current sheets are unstable and secondary islands appear. The critical aspect ratio for the unstable Sweet-Parker thin current sheet is around 65. The larger the Lundquist number is, the thinner the Sweet-Parker sheet, and the more secondary islands appear. These secondary islands are ejected out along the current sheet, grow bigger with time and coalesce with each other in the later stage. The reconnection rate of the current sheet has been increased a lot due to secondary instabilities. The peak reeonnection rates in each reconneetion processes for different Lundquist number are picked about to study the relationship between the Lundquist number and the reconnection rate, which has been found no longer scales with
A coupled "AB" system: Rogue waves and modulation instabilities.
Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N
2015-10-01
Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.
Spondylolisthesis and Posterior Instability
Energy Technology Data Exchange (ETDEWEB)
Niggemann, P.; Beyer, H.K.; Frey, H.; Grosskurth, D. (Privatpraxis fuer Upright MRT, Koeln (Germany)); Simons, P.; Kuchta, J. (Media Park Klinik, Koeln (Germany))
2009-04-15
We present the case of a patient with a spondylolisthesis of L5 on S1 due to spondylolysis at the level L5/S1. The vertebral slip was fixed and no anterior instability was found. Using functional magnetic resonance imaging (MRI) in an upright MRI scanner, posterior instability at the level of the spondylolytic defect of L5 was demonstrated. A structure, probably the hypertrophic ligament flava, arising from the spondylolytic defect was displaced toward the L5 nerve root, and a bilateral contact of the displaced structure with the L5 nerve root was shown in extension of the spine. To our knowledge, this is the first case described of posterior instability in patients with spondylolisthesis. The clinical implications of posterior instability are unknown; however, it is thought that this disorder is common and that it can only be diagnosed using upright MRI.
Csernai, László P; Papp, G
1995-01-01
The evolution of dynamical perturbations is examined in nuclear multifragmentation in the frame of Vlasov equation. Both plane wave and bubble type of perturbations are investigated in the presence of surface (Yukawa) forces. An energy condition is given for the allowed type of instabilities and the time scale of the exponential growth of the instabilities is calculated. The results are compared to the mechanical spinodal region predictions. PACS: 25.70 Mn
Instability theory of the Navier-Stokes-Poisson equations
Jang, Juhi
2011-01-01
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \\gamma < 4/3$.
Simple model with damping of the mode-coupling instability
Energy Technology Data Exchange (ETDEWEB)
Pestrikov, D.V. [AN SSSR, Novosibirsk (Russian Federation). Inst. Yadernoj Fiziki
1996-08-01
In this paper we use a simple model to study the suppression of the transverse mode-coupling instability. Two possibilities are considered. One is due to the damping of particular synchrobetatron modes, and another - due to Landau damping, caused by the nonlinearity of betatron oscillations. (author)
Various regimes of instability and formation of coastal eddies along the shelf bathymetry
Cimoli, Laura; Stegner, Alexandre; Roullet, Guillaume
2016-04-01
The impact of shelf slope on the stability of coastal currents and the nonlinear formation of coastal meanders and eddies are investigated by linear analysis and numerical simulations using an idealized channel configuration of the ROMS model. The impact of the shelf bathymetry leads to different regimes of instability of coastal currents that can both enhance or prevent the cross-shore transport. While keeping unchanged a coastal jet, we tested its unstable evolution for various depth and topographic slopes. Unlike standard linear stability analysis devoted to the very first stage of instability we focus on the non-linear end state, i.e. the formation of coastal eddies or meanders, to classify the various dynamical regimes. Two dimensionless numbers are used to quantify the parameter space of theses various regimes: the vertical aspect ratio gamma and the topographic parameter Tp, which is defined as the ratio of the topographic Rossby waves speed over the jet speed and is proportional to the shelf slope. We found four distinct regimes of instability, namely: standard baroclinic instability, horizontal shear instability, trapped coastal instability and quasi-stable jet. Our results show that Tp is the key parameter that controls the non-linear saturation of the coastal current, while gamma controls the transition from the standard baroclinic instability to the horizontal shear instability. Moreover, our analysis exhibit a new regime of formation of submeso-scale eddies. Contrary to the standard baroclinic instability regime, these eddies are trapped over the slope and never escape off-shore.
Interfacial and near interfacial crack growth phenomena in metal bonded alumina
Energy Technology Data Exchange (ETDEWEB)
Kruzic, Jamie Joseph [Univ. of California, Berkeley, CA (United States)
2001-01-01
Metal/ceramic interfaces can be found in many engineering applications including microelectronic packaging, multi-layered films, coatings, joints, and composite materials. In order to design reliable engineering systems that contain metal/ceramic interfaces, a comprehensive understanding of interfacial and near interfacial failure mechanisms is necessary.
Interfacial and near interfacial crack growth phenomena in metal bonded alumina
Energy Technology Data Exchange (ETDEWEB)
Kruzic, Jamie Joseph
2002-03-01
Metal/ceramic interfaces can be found in many engineering applications including microelectronic packaging, multi-layered films, coatings, joints, and composite materials. In order to design reliable engineering systems that contain metal/ceramic interfaces, a comprehensive understanding of interfacial and near interfacial failure mechanisms is necessary.
Real world ocean rogue waves explained without the modulational instability
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-01-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. PMID:27323897
Rayleigh-Taylor instability in soft elastic layers
Riccobelli, D.; Ciarletta, P.
2017-04-01
This work investigates the morphological stability of a soft body composed of two heavy elastic layers attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the selection of different patterns as well as their nonlinear evolution, unveiling the interplay between elastic and geometric effects for their formation. Unlike similar gravity-induced shape transitions in fluids, such as the Rayleigh-Taylor instability, we prove that the nonlinear elastic effects saturate the dynamic instability of the bifurcated solutions, displaying a rich morphological diagram where both digitations and stable wrinkling can emerge. The results of this work provide important guidelines for the design of novel soft systems with tunable shapes, with several applications in engineering sciences. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
Landau Damping of Beam Instabilities by Electron Lenses
Energy Technology Data Exchange (ETDEWEB)
Shiltsev, V. [Fermilab; Alexahin, Yuri; Burov, A. [Fermilab; Valishev, A. [Fermilab
2017-06-26
Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers and use of chromatic effects, become less effective and insufficient. We show that, in contrast, Lorentz forces of a low-energy, a magnetically stabilized electron beam, or "electron lens", easily introduces transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. It is also important that, unlike other nonlinear elements, the electron lens provides the frequency spread mainly at the beam core, thus allowing much higher frequency spread without lifetime degradation. For the parameters of the Future Circular Collider, a single conventional electron lens a few meters long would provide stabilization superior to tens of thousands of superconducting octupole magnets.
Real world ocean rogue waves explained without the modulational instability
Fedele, Francesco; Brennan, Joseph; Ponce de León, Sonia; Dudley, John; Dias, Frédéric
2016-06-01
Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas.
Interfacial area and interfacial transfer in two-phase systems. DOE final report
Energy Technology Data Exchange (ETDEWEB)
Ishii, Mamoru; Hibiki, T.; Revankar, S.T.; Kim, S.; Le Corre, J.M.
2002-07-01
In the two-fluid model, the field equations are expressed by the six conservation equations consisting of mass, momentum and energy equations for each phase. The existence of the interfacial transfer terms is one of the most important characteristics of the two-fluid model formulation. The interfacial transfer terms are strongly related to the interfacial area concentration and to the local transfer mechanisms such as the degree of turbulence near interfaces. This study focuses on the development of a closure relation for the interfacial area concentration. A brief summary of several problems of the current closure relation for the interfacial area concentration and a new concept to overcome the problem are given.
Thin film instability with thermal noise
Diez, Javier A; Fernández, Roberto
2016-01-01
We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid film upon a solid substrate. These fluctuations are represented as a standard Brownian motion that can be added to the deterministic equation for the film thickness within the lubrication approximation. Here, we consider that while the noise term is white in time, it is coloured in space. This allows for the introduction of a finite correlation length in the description of the randomized intermolecular interaction. Together with the expected spatial periodicity of the flow, we find a dimensionless parameter, $\\beta$, that accounts for the relative importance of the spatial correlation. We perform here the linear stability analysis (LSA) of the film under the influence of both terms, and find the corresponding power spectra for the amplitudes of the normal modes of the instability. We compare this theoretical result with the numerical simulations of the complete non-linear problem, and find a good ag...
Thermal instability in the interstellar medium
Directory of Open Access Journals (Sweden)
J. Ghanbari
2000-06-01
Full Text Available This study demonstrates how thermal structures in the interstellar medium can emerge as a result of thermal instability. For a two-dimensional case, the steady state thermal structures was investigeted and it was shown that a large class of solutions exist. For a one –dimensional case the conductivity was found to be negligible. The effects of to cal cooling on the thermal instability were explored in some depth. In this case analytical results for time-dependent cooling function were presented, too. We studied nonlinear wave phenomena in thermal fluid systems, with a particular emphasis on presenting analytical results. When conductivity is proportional to temperature, the beliavior of thermal waves is soliton like. For slow thermal waves, approximate analytical results were presented. Extensions of this work are discussed briefly, together with possible astrophysical applications.
Propagating Instabilities in Solids
Kyriakides, Stelios
1998-03-01
Instability is one of the factors which limit the extent to which solids can be loaded or deformed and plays a pivotal role in the design of many structures. Such instabilities often result in localized deformation which precipitates catastrophic failure. Some materials have the capacity to recover their stiffness following a certain amount of localized deformation. This local recovery in stiffness arrests further local deformation and spreading of the instability to neighboring material becomes preferred. Under displacement controlled loading the propagation of the transition fronts can be achieved in a steady-state manner at a constant stress level known as the propagation stress. The stresses in the transition fronts joining the highly deformed zone to the intact material overcome the instability nucleation stresses and, as a result, the propagation stress is usually much lower than the stress required to nucleate the instability. The classical example of this class of material instabilities is L/"uders bands which tend to affect mild steels and other metals. Recent work has demonstrated that propagating instabilities occur in several other materials. Experimental and analytical results from four examples will be used to illustrate this point: First the evolution of L=FCders bands in mild steel strips will be revisited. The second example involves the evolution of stress induced phase transformations (austenite to martensite phases and the reverse) in a shape memory alloy under displacement controlled stretching. The third example is the crushing behavior of cellular materials such as honeycombs and foams made from metals and polymers. The fourth example involves the axial broadening/propagation of kink bands in aligned fiber/matrix composites under compression. The microstructure and, as a result, the micromechanisms governing the onset, localization, local arrest and propagation of instabilities in each of the four materials are vastly different. Despite this
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
EFFECTS OF DIFFERENT NUMERICAL INTERFACE METHODS ON HYDRODYNAMICS INSTABILITY
Energy Technology Data Exchange (ETDEWEB)
FRANCOIS, MARIANNE M. [Los Alamos National Laboratory; DENDY, EDWARD D. [Los Alamos National Laboratory; LOWRIE, ROBERT B. [Los Alamos National Laboratory; LIVESCU, DANIEL [Los Alamos National Laboratory; STEINKAMP, MICHAEL J. [Los Alamos National Laboratory
2007-01-11
The authors compare the effects of different numerical schemes for the advection and material interface treatments on the single-mode Rayleigh-Taylor instability, using the RAGE hydro-code. The interface growth and its surface density (interfacial area) versus time are investigated. The surface density metric shows to be better suited to characterize the difference in the flow, than the conventional interface growth metric. They have found that Van Leer's limiter combined to no interface treatment leads to the largest surface area. Finally, to quantify the difference between the numerical methods they have estimated the numerical viscosity in the linear-regime at different scales.
Snap-Through Instability of Graphene on Substrates
Directory of Open Access Journals (Sweden)
Li Teng
2009-01-01
Full Text Available Abstract We determine the graphene morphology regulated by substrates with herringbone and checkerboard surface corrugations. As the graphene–substrate interfacial bonding energy and the substrate surface roughness vary, the graphene morphology snaps between two distinct states: (1 closely conforming to the substrate and (2 remaining nearly flat on the substrate. Since the graphene morphology is strongly tied to the electronic properties of graphene, such a snap-through instability of graphene morphology can lead to desirable graphene electronic properties that could potentially enable graphene-based functional electronic components (e.g. nano-switches.
Taming of Modulation Instability by Spatio-Temporal Modulation of the Potential
Kumar, S; Botey, M; Staliunas, K
2015-01-01
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the manipulation of the modulation instability is of primary importance in controlling and manipulating the character of spatial patterns initiated by that instability. We show that the spatio-temporal periodic modulation of the potential of the spatially extended system results in a modification of its pattern forming instability. Depending on the modulation character the instability can be partially suppressed, can change its spectrum (for instance the long wave instability can transform into short wave instability), can split into two, or can be completely eliminated. The latter result is of especial practical interest, as can be used to stabilize the intrinsically unstable system. The result bears general character, as it is shown here on a universal model of Complex Ginzburg-L...
MHD instabilities developing in a conductor exploding in the skin effect mode
Oreshkin, V. I.; Chaikovsky, S. A.; Datsko, I. M.; Labetskaya, N. A.; Mesyats, G. A.; Oreshkin, E. V.; Ratakhin, N. A.; Rybka, D. V.
2016-12-01
The results of experiments with exploding copper conductors, performed on the MIG facility (providing currents of amplitude of about 2.5 MA and rise time of 100 ns), are analyzed. With an frame optical camera, large-scale instabilities of wavelength 0.2-0.5 mm were detected on the conductor surface. The instabilities show up as plasma "tongues" expanding with a sound velocity in the opposite direction to the magnetic field gradient. Analysis performed using a two-dimensional MHD code has shown that the structures observed in the experiments were formed most probably due to flute instabilities. The growth of flute instabilities is predetermined by the development of thermal instabilities near the conductor surface. The thermal instabilities arise behind the front of the nonlinear magnetic diffusion wave propagating through the conductor. The wavefront on its own is not subject to thermal instabilities.
Polymer behavior under the influence of interfacial interactions
Kropka, Jamie Michael
The properties of polymers, thin films or bulk, are profoundly influenced by interactions at interfaces with dissimilar materials. Thin, supported, polymer films are subject to interfacial instabilities, due largely to competing intermolecular forces, that cause them to rupture and dewet the substrate. The addition of nanoparticles (such as clay sheets, metallic or semiconductor nanocrystals, carbon nanotubes, etc.) to polymers can substantially affect bulk properties, such as the glass transition and viscosity, and influence the processability of the material. In this dissertation, we contribute to a fundamental understanding of the role of interfacial interactions on both the instabilities exhibited by polymer thin films and the properties displayed by polymer-nanoparticle mixtures. While conditions under which the destabilization of compositionally homogeneous thin films occurs are relatively well understood, the mechanisms of film stabilization in many two-component thin film systems are still unresolved. We demonstrate that the addition of a miscible component to an unstable film can provide an effective means of stabilization. The details of the stabilization mechanism are understood in terms of the compositional dependence of both the macroscopic wetting parameters and the effective interface potential for the system. We find that the suppression of dewetting in the system is not an equilibrium stabilization process and propose a mechanism by which the increased resistance to dewetting may occur. There is also significant interest in understanding the extraordinary property enhancement of polymers that are enabled by the addition of only small concentrations of nanoparticles. If these effects could be distilled down to a few simple rules, they could be exploited in the design of materials for specific applications. In this work, the influence of C60 nanoparticles on the bulk dynamical properties of three polymers is examined. Based on the findings from a
THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
SHANG MEI; GUO YONG-XIN
2001-01-01
We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.
Gotoda, Hiroshi; Amano, Masahito; Miyano, Takaya; Ikawa, Takuya; Maki, Koshiro; Tachibana, Shigeru
2012-12-01
We characterize complexities in combustion instability in a lean premixed gas-turbine model combustor by nonlinear time series analysis to evaluate permutation entropy, fractal dimensions, and short-term predictability. The dynamic behavior in combustion instability near lean blowout exhibits a self-affine structure and is ascribed to fractional Brownian motion. It undergoes chaos by the onset of combustion oscillations with slow amplitude modulation. Our results indicate that nonlinear time series analysis is capable of characterizing complexities in combustion instability close to lean blowout.
The Magneto-Rotational Decay Instability in Keplerian Disks
Shtemler, Yuri; Mond, Michael
2013-01-01
The saturation of the magnetorotational (MRI) instability in thin Keplerian disks through three wave resonant interactions is introduced and discussed. That mechanism is a natural generalization of the fundamental decay instability discovered five decades ago for infinite, homogeneous and immovable plasmas. The decay instability relies on the energy transfer from the MRI to stable slow Alfv'en-Coriolis (AC) as well as magnetosonic (MS) waves. A second order forced Duffing amplitude equation for the initially unstable MRI as well as two first order equations for the other two waves are derived. The solutions of those equations exhibit bounded bursty nonlinear oscillations for the MRI as well as unbounded growth for the linearly stable slow AC and MS perturbations, thus giving rise to the magneto-rotational decay instability (MRDI).
Transverse electron-scale instability in relativistic shear flows
Alves, E P; Fonseca, R A; Silva, L O
2015-01-01
Electron-scale surface waves are shown to be unstable in the transverse plane of a shear flow in an initially unmagnetized plasma, unlike in the (magneto)hydrodynamics case. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroom-like electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. Macroscopic ($\\gg c/\\omega_{pe}$) fields are shown to be generated by these microscopic shear instabilities, which are relevant for particle acceleration, radiation emission and to seed MHD processes at long time-scales.
Dark solitons, dispersive shock waves, and transverse instabilities
Hoefer, M A
2011-01-01
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev-Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS / GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields 1) the maximum growth rate and associated wavenumber of unstable perturbations; and 2) the separatrix between convective and absolute instabilities. The latter result is used to study the transition between convective and absolute instabilities of oblique dispersive shock waves (DSWs). Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS / GP equation. The instability properties of oblique DSWs are found to be dir...
Campbell, Bryce; Hendrickson, Kelli; Liu, Yuming; Subramani, Hariprasad
2014-11-01
For gas-liquid flows through pipes and channels, a flow regime (referred to as slug flow) may occur when waves form at the interface of a stratified flow and grow until they bridge the pipe diameter trapping large elongated gas bubbles within the liquid. Slug formation is often accompanied by strong nonlinear wave-wave interactions, wave breaking, and gas entrainment. This work numerically investigates the fully nonlinear interfacial evolution of a two-phase density/viscosity stratified flow through a horizontal channel. A Navier-Stokes flow solver coupled with a conservative volume-of-fluid algorithm is use to carry out high resolution three-dimensional simulations of a turbulent gas flowing over laminar (or turbulent) liquid layers. The analysis of such flows over a range of gas and liquid Reynolds numbers permits the characterization of the interfacial stresses and turbulent flow statistics allowing for the development of physics-based models that approximate the coupled interfacial-turbulent interactions and supplement the heuristic models built into existing industrial slug simulators.
Modulational instability in wind-forced waves
Brunetti, Maura
2014-01-01
We consider the wind-forced nonlinear Schroedinger (NLS) equation obtained in the potential flow framework when the Miles growth rate is of the order of the wave steepness. In this case, the form of the wind-forcing terms gives rise to the enhancement of the modulational instability and to a band of positive gain with infinite width. This regime is characterised by the fact that the ratio between wave momentum and norm is not a constant of motion, in contrast to what happens in the standard case where the Miles growth rate is of the order of the steepness squared.
Instability of Bucket Foundations during Installation
DEFF Research Database (Denmark)
Madsen, Søren; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo
The bucket foundation is an upcoming technology for offshore wind turbines. The bucket foundation is a large cylindrical monopod foundation constructed as a thin steel shell structure. A bucket foundation does not require heavy installation equipment since it is installed by suction forces....... The combination of a thin shell structure and suction forces leads to the fact that instability, in form of buckling, becomes a crucial issue during installation. The hydrostatic buckling pressure of the bucket foundation is addressed using three-dimensional, non-linear finite element analysis. The results...
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Input saturation in nonlinear multivariable processes resolved by nonlinear decoupling
Directory of Open Access Journals (Sweden)
Jens G. Balchen
1995-04-01
Full Text Available A new method is presented for the resolution of the problem of input saturation in nonlinear multivariable process control by means of elementary nonlinear decoupling (END. Input saturation can have serious consequences particularly in multivariable control because it may lead to very undesirable system behaviour and quite often system instability. Many authors have searched for systematic techniques for designing multivariable control systems in which saturation may occur in any of the control variables (inputs, manipulated variables. No generally accepted method seems to have been presented so far which gives a solution in closed form. The method of elementary nonlinear decoupling (END can be applied directly to the case of saturation control variables by deriving as many control strategies as there are combinations of saturating control variables. The method is demonstrated by the multivariable control of a simulated Fluidized Catalytic Cracker (FCC with very convincing results.
Patterns, Instabilities, Colors, and Flows in Vertical Foam Films
Yilixiati, Subinuer; Wojcik, Ewelina; Zhang, Yiran; Pearsall, Collin; Sharma, Vivek
2015-03-01
Foams find use in many applications in daily life, industry and biology. Examples include beverages, firefighting foam, cosmetics, foams for oil recovery and foams formed by pollutants. Foams are collection of bubbles separated by thin liquid films that are stabilized against drainage by the presence of surfactant molecules. Drainage kinetics and stability of the foam are strongly influenced by surfactant type, addition of particles, proteins and polymers. In this study, we utilize the thin film interference colors as markers for identifying patterns, instabilities and flows within vertical foam films. We experimentally study the emergence of thickness fluctuations near the borders and within thinning films, and study how buoyancy, capillarity and gravity driven instabilities and flows, are affected by variation in bulk and interfacial physicochemical properties dependent on the choice of constituents.
Neutrino beam plasma instability
Indian Academy of Sciences (India)
Vishnu M Bannur
2001-10-01
We derive relativistic ﬂuid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these ﬂuid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino ﬂux, but becomes stronger for weakly relativistic neutrino ﬂux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25 and in the other limit electroweak unstable mode takes over.
DEFF Research Database (Denmark)
Langie, Sabine A S; Koppen, Gudrun; Desaulniers, Daniel
2015-01-01
, genome instability can be defined as an enhanced tendency for the genome to acquire mutations; ranging from changes to the nucleotide sequence to chromosomal gain, rearrangements or loss. This review raises the hypothesis that in addition to known human carcinogens, exposure to low dose of other...... scientists aware of the increasing need to unravel the underlying mechanisms via which chemicals at low doses can induce genome instability and thus promote carcinogenesis.......Genome instability is a prerequisite for the development of cancer. It occurs when genome maintenance systems fail to safeguard the genome's integrity, whether as a consequence of inherited defects or induced via exposure to environmental agents (chemicals, biological agents and radiation). Thus...
Phase diagrams modified by interfacial penalties
Directory of Open Access Journals (Sweden)
Atanacković T.M.
2007-01-01
Full Text Available The conventional forms of phase diagrams are constructed without consideration of interfacial energies and they represent an important tool for chemical engineers and metallurgists. If interfacial energies are taken into consideration, it is intuitively obvious that the regions of phase equilibria must become smaller, because there is a penalty on the formation of interfaces. We investigate this phenomenon qualitatively for a one-dimensional model, in which the phases occur as layers rather than droplets or bubbles. The modified phase diagrams are shown in Chapters 3 and 4.
Mixing through shear instabilities
Brüggen, M
2000-01-01
In this paper we present the results of numerical simulations of the Kelvin-Helmholtz instability in a stratified shear layer. This shear instability is believed to be responsible for extra mixing in differentially rotating stellar interiors and is the prime candidate to explain the abundance anomalies observed in many rotating stars. All mixing prescriptions currently in use are based on phenomenological and heuristic estimates whose validity is often unclear. Using three-dimensional numerical simulations, we study the mixing efficiency as a function of the Richardson number and compare our results with some semi-analytical formalisms of mixing.
Athermal nonlinear elastic constants of amorphous solids.
Karmakar, Smarajit; Lerner, Edan; Procaccia, Itamar
2010-08-01
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities such as plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elastoplasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of our calculations we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place.
Nonlinearity and hysteresis of resonant strain gauges
Gui, Chengqun; Legtenberg, Rob; Tilmans, Harrie A.C.; Fluitman, Jan H.J; Elwenspoek, Miko
1995-01-01
Nonlinearity and hysteresis effects of electrostatically activated, voltage driven resonant microbridges have been studied theoretically and experimentally. It is shown, that, in order to avoid vibration instability and hysteresis to occur, the choices of the ax. and d.c. driving voltages and of the
Nonlinearity and hysteresis of resonant strain gauges
Gui, Chengqun; Legtenberg, Rob; Tilmans, Harrie A.C.; Fluitman, Jan H.J; Elwenspoek, Miko
1998-01-01
The nonlinearity and hysteresis effects of the electrostatically activated voltage-driven resonant microbridges have been studied theoretically and experimentally. It is shown that in order to avoid vibration instability and hysteresis to occur, the choices of the ac and dc driving voltages and of t
Modulational instability of two-component Bose-Einstein condensates in an optical lattice
Jin, G R; Nahm, K; Jin, Guang-Ri; Kim, Chul Koo; Nahm, Kyun
2004-01-01
We study modulational instability of two-component Bose-Einstein condensates in a deep optical lattice, which is modelled as a coupled discrete nonlinear Schr\\"{o}dinger equation. The excitation spectrum and the modulational instability condition of the total system are presented analytically. In the long-wavelength limit, our results agree with the homogeneous two-component Bose-Einstein condensates case. The discreteness effects result in the appearance of the modulational instability for the condensates in miscible region. The numerical calculations confirm our analytical results and show that the interspecies coupling can transfer the instability from one component to another.
Interfacial wave behavior in oil-water channel flows: Prospects for a general understanding
Energy Technology Data Exchange (ETDEWEB)
McCready, M.J.; Uphold, D.D.; Gifford, K.A. [Univ. of Notre Dame, IN (United States)
1997-12-31
Oil-water pressure driven channel flow is examined as a model for general two-layer flows where interfacial disturbances are important. The goal is to develop sufficient understanding of this system so that the utility and limitations of linear and nonlinear theories can be known a priori. Experiments show that sometimes linear stability is useful at predicting the steady or dominant evolving waves. However in other situations there is no agreement between the linearly fastest growing wave and the spectral peak. An interesting preliminary result is that the bifurcation to interfacial waves is supercritical for all conditions that were studied for an oil-water channel flow, gas-liquid channel flow and two-liquid Couette flow. However, three different mechanisms are dominant for each of these three situations.
Interfacial rheology and emulsion stability in model systems
Pratt, G
1998-01-01
Measurements of thermodynamic interfacial tension sigma at a non-equilibrium surfactant adsorption have been made using a pulsed drop rheometer. The pulsed drop rheometer is based on an instantaneous expansion of a water droplet in oil. After perturbation an interfacial relaxation occurs, the interfacial pressure decay is followed as a function of time using a sensitive pressure transducer. The difference in pressure across a curved interface and the interfacial tension are directly related. Interfacial tension decays can be obtained above and below the surfactants CMC. The interfacial tension decays obtained were fitted to known relaxation mechanisms, and found generally to fit diffusional mechanisms. The funnel technique involves expansion of the interface through a funnel, the interfacial tension decays are followed directly. The results were found to be analogous to measurements made by the pulsed drop. Measurements have been made of the interfacial shear viscosity of a polymeric surfactant at the oil / w...
Inverse Saffman-Taylor instability in Hele-Shaw experiments using micro-particles
Zoueshtiagh, Farzam; Bihi, Ilyesse; Butler, Jason; Faille, Christine; Baudoin, Michaël
2016-11-01
Saffman-Taylor instability can occur when a low viscosity fluid displaces one of higher viscosity. It results from the decrease of the flow resistance as the fluid of lower viscosity replaces the more viscous one. This Saffman-Taylor instability is revisited experimentally for the inverse case of a viscous fluid displacing air when partially wetting particles are lying on the walls. Though the inverse case is otherwise stable, the presence of the particles results in a fingering instability at low capillary number. This capillary-driven instability is driven by the integration of particles into the interface which results from the minimization of the interfacial energy. We acknowledge the support from the Marie Curie International Research Staff Exchange Scheme Fellowship ("Patterns and Surfaces" No. 269207) within the 7th European Community Framework Programme.
A general theory of mechanical instabilities in soft solids
Hohlfeld, Evan; Mahadevan, L.
2011-03-01
Some instabilities in soft solids, e.g. buckling and wrinkling, can be detected in linearized analysis. Surprisingly, linearly stable configurations can still have nonlinear instabilities with strictly zero energy barrier. Two examples are cavitation (formation of voids) and sulcification (formation of sharply creased free surface folds), wherein singularities nucleate and grow when a critical strain is achieved. Here we present the first general theory of stability in nonlinearly elastic materials. The theory predicts when singularities spontaneously form, irrespective of linearized analysis, and how these can be controlled with geometry. Such ``hidden'' instabilities arise from the scale-free geometric and constitutive nonlinearities common in soft materials, and can be understood as scale symmetry breaking processes in simple cases. More deeply, even buckling and wrinkling can be traced back to scale-free linear instabilities (loss of ellipticity at an interface) as was first explained by M. A. Biot. We illustrate the theory with simulations and experiments on sulcification. Time allowing we will also discuss fracture and delamination.
Surface and interfacial tension measurement, theory, and applications
Hartland, Stanley
2004-01-01
This edited volume offers complete coverage of the latest theoretical, experimental, and computer-based data as summarized by leading international researchers. It promotes full understanding of the physical phenomena and mechanisms at work in surface and interfacial tensions and gradients, their direct impact on interface shape and movement, and their significance to numerous applications. Assessing methods for the accurate measurement of surface tension, interfacial tension, and contact angles, Surface and Interfacial Tension presents modern simulations of complex interfacial motions, such a
The Constrained Vapor Bubble Experiment - Interfacial Flow Region
Kundan, Akshay; Wayner, Peter C., Jr.; Plawsky, Joel L.
2015-01-01
Internal heat transfer coefficient of the CVB correlated to the presence of the interfacial flow region. Competition between capillary and Marangoni flow caused Flooding and not a Dry-out region. Interfacial flow region growth is arrested at higher power inputs. 1D heat model confirms the presence of interfacial flow region. 1D heat model confirms the arresting phenomena of interfacial flow region Visual observations are essential to understanding.
The azimuthal magnetorotational instability (AMRI)
Ruediger, G; Schultz, M; Hollerbach, R; Stefani, F
2013-01-01
We consider the interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfven frequency of the field are of the same order almost independent of the magnetic Prandtl number Pm. For the very steep rotation law \\Omega\\propto R^{-2} (the Rayleigh limit) this Azimuthal MagnetoRotational Instability (AMRI) scales with the ordinary Reynolds number and the Hartmann number, which allows a laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container. The growth rate of AMRI scales with \\Omega^2 in the low-conductivity limit and with \\Omega in the high-conductivity limit. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers between 0.05 and unity. We find that the magnetic energy scales with the magnetic Reynolds number Rm, while th...
Modulation instability of structured-light beams in negative-index metamaterials
Silahli, Salih Z; Litchinitser, Natalia M
2016-01-01
One of the most fundamental properties of isotropic negative-index metamaterials, namely opposite directionality of the Poynting vector and the wavevector, enable many novel linear and nonlinear regimes of light-matter interactions. Here, we predict distinct characteristics of azimuthal modulation instability of optical vortices with different topological charges in negative-index metamaterials with Kerr-type and saturable nonlinearity. We derive an analytical expression for the spatial modulation-instability gain for the Kerr-nonlinearity case and show that a specific condition relating the diffraction and the nonlinear lengths must be fulfilled for the azimuthal modulation instability to occur. Finally, we investigate the rotation of the necklace beams due to the transfer of orbital angular momentum of the generating vortex onto the movement of solitary necklace beams. We show that the direction of rotation is opposite in the positive- and negative-index materials.
Burcham, F. W., Jr.; Zeller, J. R.
1984-01-01
An instability in the nozzle of the F100 engine, equipped with a digital electronic engine control (DEEC), was observed during a flight evaluation on an F-15 aircraft. The instability occurred in the upper left hand corner (ULMC) of the flight envelope during augmentation. The instability was not predicted by stability analysis, closed-loop simulations of the the engine, or altitude testing of the engine. The instability caused stalls and augmentor blowouts. The nozzle instability and the altitude testing are described. Linear analysis and nonlinear digital simulation test results are presented. Software modifications on further flight test are discussed.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Wave train generation of solitons in systems with higher-order nonlinearities.
Mohamadou, Alidou; LatchioTiofack, C G; Kofané, Timoléon C
2010-07-01
Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.
New observations of ionospheric instabilities in the equatorial electrojet
Alken, P.; Maus, S.
2009-12-01
The equatorial electrojet (EEJ) is an intense current system flowing along the magnetic equator in the ionospheric E-region on the day-side. Early attempts to model the EEJ found that ionospheric instabilities led to significant changes in the current which had to be accounted for. Early modelers used ad-hoc empirical correction factors in the relevant ionospheric parameters to attempt to account for instability effects. Modern EEJ models continue to use these correction factors, which are still not well understood theoretically. In the last decade, a wealth of new data has been recorded by both satellites and ground radars which allows us to revisit the issue of modeling these ionospheric instabilities. In this work, we use radar and magnetic field measurements at Jicamarca in addition to magnetometer measurements from the CHAMP satellite to study the effects of ionospheric instabilities on the EEJ. We find that the effects of ionospheric instabilities lead to non-linear behavior between the eastward electric field strength and the resulting electrojet current. As predicted, the ratio of current to electric field is highest for westward and weak eastward electric fields, and the ratio decreases with stronger eastward electric fields. Quantifying this non-linearity should help improve the accuracy of equatorial electrodynamic models.
Interfacial Reactions of Metal Oxide Stack Dielectrics Studied with Medium Energy Ion Scattering
Copel, M.; Reuter, M. C.; Cartier, E.; Callegari, A.; Guha, S.; Gousev, E. P.; Jamison, P.; Narayanan, V.; Neumayer, D.
2003-03-01
Application of a metal oxide as a gate dielectric for Si CMOS requires an understanding of the materials reactions that occur with thermal processing. A number of metal oxides have been examined for use as a gate dielectric, with varying degrees of reactivity. Reactions between Y and La oxides and SiO2 are facile, forming interfacial silicates that can extend many nanometers. For the case of Y_2O_3, this reaction can completely consume an SiO2 or SiO_xNy buffer layer, resulting in a silicate/Si(001) interface with no interfacial layer detectable by medium energy ion scattering (MEIS). In contrast, Zr and Hf oxides tend to remain unmixed with SiO_2, due to either sluggish kinetics or instability of the silicates. Interfacial reaction zones can be extremely limited, extending less than 1 nanometer for chemically deposited films. We will report MEIS results for gate dielectric stacks, using in situ processing to illustrate the materials reactions that are commonly encountered.
Gelation and interfacial behaviour of vegetable proteins
Vliet, T. van; Martin, A.H.; Bos, M.A.
2002-01-01
Recent studies on gelation and interfacial properties of vegetable protiens are reviewed. Attention is focused on legume proteins, mainly soy proteins, and on wheat proteins. The rheological properteis of vegetable protein gels as a function of heating time or temperature is discussed as well as the
Molecular structure and interfacial behaviour of polymers
Lent, van B.
1989-01-01
The aim of this study was to investigate the influence of the molecular structure on the interfacial behaviour of polymers. Theoretical models were developed for three different systems. All these models are based on the self-consistent field theory of Scheutjens and Fleer for the
[Importance of interfacial characteristics in pharmaceutical technology].
Dredán, Judit; Csóka, Gabriella; Marton, Sylvia; Antal, István
2003-01-01
Since drug release from the dosage forms has priority to absorption from the gastrointestinal system, physico-chemical characterisation of pharmaceutical systems is essential during the development of an optimal formulation with high efficacy and quality. Interfacial parameters of several pharmaceutical excipients were studied regarding their possible modifying effect on drug release from the dosage form. These inactive ingredients may influence the interfacial phenomena of the drug carrier system, which behaviour determines both the efficacy and the quality of the pharmaceutical preparation In this work authors deal mainly with the two introducing steps of the LADME model influenced by interfacial parameters on them, namely with the liberation of drug from the dosage form and with the characteristics influencing the absorption through biological membranes, respectively. The objective of the present work was to study modifying effects of excipients on drug liberation in connection with their physical and chemical characteristics such as interfacial tension of solid and liquid phases, wetting contact angle of solid phase and--a calculated quantity,--adhesion tension of the solid particles.
Exchange bias mediated by interfacial nanoparticles (invited)
Energy Technology Data Exchange (ETDEWEB)
Berkowitz, A. E., E-mail: aberk@ucsd.edu [Department of Physics, University of California, San Diego, La Jolla, California 92093 (United States); Center for Magnetic Recording Research, University of California, California 92093 (United States); Sinha, S. K. [Department of Physics, University of California, San Diego, La Jolla, California 92093 (United States); Fullerton, E. E. [Center for Magnetic Recording Research, University of California, California 92093 (United States); Smith, D. J. [Department of Physics, Arizona State University, Tempe, Arizona 85287 (United States)
2015-05-07
The objective of this study on the iconic exchange-bias bilayer Permalloy/CoO has been to identify those elements of the interfacial microstructure and accompanying magnetic properties that are responsible for the exchange-bias and hysteretic properties of this bilayer. Both epitaxial and polycrystalline samples were examined. X-ray and neutron reflectometry established that there existed an interfacial region, of width ∼1 nm, whose magnetic properties differed from those of Py or CoO. A model was developed for the interfacial microstructure that predicts all the relevant properties of this system; namely; the temperature and Permalloy thickness dependence of the exchange-bias, H{sub EX}, and coercivity, H{sub C}; the much smaller measured values of H{sub EX} from what was nominally expected; the different behavior of H{sub EX} and H{sub C} in epitaxial and polycrystalline bilayers. A surprising result is that the exchange-bias does not involve direct exchange-coupling between Permalloy and CoO, but rather is mediated by CoFe{sub 2}O{sub 4} nanoparticles in the interfacial region.
Gelation and interfacial behaviour of vegetable proteins
Vliet, van T.; Martin, A.H.; Bos, M.A.
2002-01-01
Recent studies on gelation and interfacial properties of vegetable proteins are reviewed. Attention is focused on legume proteins, mainly soy proteins, and on wheat proteins. The rheological properties of vegetable protein gels as a function of heating time or temperature is discussed as well as the
Gelation and interfacial behaviour of vegetable proteins
Vliet, T. van; Martin, A.H.; Bos, M.A.
2002-01-01
Recent studies on gelation and interfacial properties of vegetable protiens are reviewed. Attention is focused on legume proteins, mainly soy proteins, and on wheat proteins. The rheological properteis of vegetable protein gels as a function of heating time or temperature is discussed as well as the
Shock instability in dissipative gases
Radulescu, Matei I.; Sirmas, Nick
2011-01-01
Previous experiments have revealed that shock waves in thermally relaxing gases, such as ionizing, dissociating and vibrationally excited gases, can become unstable. To date, the mechanism controlling this instability has not been resolved. Previous accounts of the D'yakov-Kontorovich instability, and Bethe-Zel'dovich-Thompson behaviour could not predict the experimentally observed instability. To address the mechanism controlling the instability, we study the propagation of shock waves in a ...
Floquet instability of a large density ratio liquid-gas coaxial jet with periodic fluctuation
Institute of Scientific and Technical Information of China (English)
LI Zhen; HU Guo-hui; ZHOU Zhe-wei
2008-01-01
By numerical simulation of basic flow, this paper extends Floquet stability analysis of interfacial flow with periodic fluctuation into large density ratio range. Sta- bility of a liquid aluminum jet in a coaxial nitrogen stream with velocity fluctuation is investigated by Chebyshev collocation method and the Floquet theory. Parametric reso- nance of the jet and the influences of different physical parameters on the instability are discussed. The results show qualitative agreement with the available experimental data.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Electromagnetic Instabilities Excited by Electron Temperature Anisotropy
Institute of Scientific and Technical Information of China (English)
陆全明; 王连启; 周艳; 王水
2004-01-01
One-dimensional particle-in-cell simulations are performed to investigate the nonlinear evolution of electromagnetic instabilities excited by the electron temperature anisotropy in homogeneous plasmas with different parameters. The results show that the electron temperature anisotropy can excite the two right-hand electromagnetic instabilities, one has the frequency higher than Ωe, the other is the whistler instability with larger amplitude,and its frequency is below Ωe. Their dispersion relations are consistent with the prediction from the cold plasma theory. In the initial growth stage (prediction from linear theory), the frequency of the dominant mode (the mode whose amplitude is large enough) of the whistler wave almost does not change, but in the saturation stage the situation is different. In the case that the ratio of electron plasma frequency to cyclotron frequency is larger than 1, the frequency of the dominant mode of the whistler wave drifts from high to low continuously. However, for the case of the ratio smaller than 1, besides the original dominant mode of the whistler wave whose frequency is about 2.6ωe, another dominant mode whose frequency is about 1.55ωe also begins to be excited at definite time,and its amplitude increases with time until it exceeds the original dominant mode.
Dust Dynamics in Kelvin-Helmholtz Instabilities
Hendrix, Tom; Keppens, Rony
2013-04-01
The Kelvin-Helmholtz instability (KHI) is a fluid instability which arises when two contacting flows have different tangential velocities. As shearing flows are very common in all sorts of (astro)physical fluid setups, the KHI is frequently encountered. In many astrophysical fluids the gas fluid in loaded with additional dust particles. Here we study the influence of these dust particles on the initiation of the KHI, as well as the effect the KHI has on the density distribution of dust species in a range of different particle sizes. This redistribution by the instability is of importance in the formation of dust structures in astrophysical fluids. To study the effect of dust on the linear and nonlinear phase of the KHI, we use the multi-fluid dust + gas module of the MPI-AMRVAC [1] code to perform 2D and 3D simulations of KHI in setups with physical quantities relevant to astrophysical fluids. A clear dependency on dust sizes is seen, with larger dust particles displaying significantly more clumping than smaller ones.
Nuclear-Coupled Flow Instabilities and Their Effects on Dryout
Energy Technology Data Exchange (ETDEWEB)
M. Ishii; X. Sunn; S. Kuran
2004-09-27
Nuclear-coupled flow/power oscillations in boiling water reactors (BWRs) are investigated experimentally and analytically. A detailed literature survey is performed to identify and classify instabilities in two-phase flow systems. The classification and the identification of the leading physical mechanisms of the two-phase flow instabilities are important to propose appropriate analytical models and scaling criteria for simulation. For the purpose of scaling and the analysis of the nonlinear aspects of the coupled flow/power oscillations, an extensive analytical modeling strategy is developed and used to derive both frequency and time domain analysis tools.
Waves and instability in a one-dimensional microfluidic array
Liu, Bin; Feng, Yan
2012-01-01
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.
Competing Turing and Faraday Instabilities in Longitudinally Modulated Passive Resonators.
Copie, François; Conforti, Matteo; Kudlinski, Alexandre; Mussot, Arnaud; Trillo, Stefano
2016-04-08
We experimentally investigate the interplay of Turing (modulational) and Faraday (parametric) instabilities in a bistable passive nonlinear resonator. The Faraday branch is induced via parametric resonance owing to a periodic modulation of the resonator dispersion. We show that the bistable switching dynamics is dramatically affected by the competition between the two instability mechanisms, which dictates two completely novel scenarios. At low detunings from resonance, switching occurs between the stable stationary lower branch and the Faraday-unstable upper branch, whereas at high detunings we observe the crossover between the Turing and Faraday periodic structures. The results are well explained in terms of the universal Lugiato-Lefever model.
Nonlinear lower hybrid modeling in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Napoli, F.; Schettini, G. [Università Roma Tre, Dipartimento di Ingegneria, Roma (Italy); Castaldo, C.; Cesario, R. [Associazione EURATOM/ENEA sulla Fusione, Centro Ricerche Frascati (Italy)
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
Institute of Scientific and Technical Information of China (English)
Jiebin Liu; Jifu Zhou
2016-01-01
The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.
Riquelme, Mario; Verscharen, Daniel
2014-01-01
We use particle-in-cell (PIC) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period, and the plasma beta is ~ 1-100. The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities. The field amplification continuously drives a pressure anisotropy with the perpendicular pressure larger than the parallel pressure, and the plasma becomes unstable to the mirror and ion cyclotron instabilities. In all cases, the nonlinear state is dominated by the mirror instability, not the ion cyclotron instability, and the plasma pressure anisotropy saturates near the threshold for the linear mirror instability. The magnetic field fluctuations initially undergo exponential growth but saturate in a secular p...
Genetic instability in Gynecological Cancer
Institute of Scientific and Technical Information of China (English)
ZHAO Qing-hua; ZHOU Hong-lin
2003-01-01
Defects of mismatch repair (MMR) genes also have beenidentified in many kinds of tumors. Loss of MMR functionhas been linked to genetic instability especially microsatelliteinstability that results in high mutation rate. In this review, wediscussed the microsatellite instability observed in thegynecological tumors. We also discussed defects in the DNAmismatch repair in these tumors and their correlation to themicrosatellite instability, as well as the gene mutations due tothe microsatellite instability in these tumors. From thesediscussion, we tried to understand the mechanism ofcarcinogenesis in gynecological tumors from the aspect ofgenetic instability due to mismatch repair defects.
Instabilities in sensory processes
Balakrishnan, J.
2014-07-01
In any organism there are different kinds of sensory receptors for detecting the various, distinct stimuli through which its external environment may impinge upon it. These receptors convey these stimuli in different ways to an organism's information processing region enabling it to distinctly perceive the varied sensations and to respond to them. The behavior of cells and their response to stimuli may be captured through simple mathematical models employing regulatory feedback mechanisms. We argue that the sensory processes such as olfaction function optimally by operating in the close proximity of dynamical instabilities. In the case of coupled neurons, we point out that random disturbances and fluctuations can move their operating point close to certain dynamical instabilities triggering synchronous activity.
Instability and internet design
Directory of Open Access Journals (Sweden)
Sandra Braman
2016-09-01
Full Text Available Instability - unpredictable but constant change in one’s environment and the means with which one deals with it - has replaced convergence as the focal problem for telecommunications policy in general and internet policy in particular. Those who designed what we now call the internet during the first decade of the effort (1969-1979, who in essence served simultaneously as its policy-makers, developed techniques for coping with instability of value for network designers today and for those involved with any kind of large-scale sociotechnical infrastructure. Analysis of the technical document series that was medium for and record of that design process reveals coping techniques that began with defining the problem and went on to include conceptual labour, social practices, and technical approaches.
Gravitational instabilities of superspinars
Pani, Paolo; Berti, Emanuele; Cardoso, Vitor
2010-01-01
Superspinars are ultracompact objects whose mass M and angular momentum J violate the Kerr bound (cJ/GM^2>1). Recent studies analyzed the observable consequences of gravitational lensing and accretion around superspinars in astrophysical scenarios. In this paper we investigate the dynamical stability of superspinars to gravitational perturbations, considering either purely reflecting or perfectly absorbing boundary conditions at the "surface" of the superspinar. We find that these objects are unstable independently of the boundary conditions, and that the instability is strongest for relatively small values of the spin. Also, we give a physical interpretation of the various instabilities that we find. Our results (together with the well-known fact that accretion tends to spin superspinars down) imply that superspinars are very unlikely astrophysical alternatives to black holes.
Magnetically-Driven Convergent Instability Growth platform on Z.
Energy Technology Data Exchange (ETDEWEB)
Knapp, Patrick; Mattsson, Thomas; Martin, Matthew; Benage, John F.,
2017-09-01
Hydrodynamic instability growth is a fundamentally limiting process in many applications. In High Energy Density Physics (HEDP) systems such as inertial confinement fusion implosions and stellar explosions, hydro instabilities can dominate the evolution of the object and largely determine the final state achievable. Of particular interest is the process by which instabilities cause perturbations at a density or material interface to grow nonlinearly, introducing vorticity and eventually causing the two species to mix across the interface. Although quantifying instabilities has been the subject of many investigations in planar geometry, few have been done in converging geometry. During FY17, the team executed six convergent geometry instability experiments. Based on earlier results, the platform was redesigned and improved with respect to load centering at installation making the installation reproducible and development of a new 7.2 keV, Co He-a backlighter system to better penetrate the liner. Together, the improvements yielded significantly improved experimental results. The results in FY17 demonstrate the viability of using experiments on Z to quantify instability growth in cylindrically convergent geometry. Going forward, we will continue the partnership with staff and management at LANL to analyze the past experiments, compare to hydrodynamics growth models, and design future experiments.
Mechanical properties and interfacial characteristics of carbon-nanotube-reinforced epoxy thin films
Xu, Xiaojing; Thwe, Moe Moe; Shearwood, Christopher; Liao, Kin
2002-10-01
Multiwalled carbon nanotubes (MWNT) reinforced epoxy composite thin films were prepared by a microfabrication process and their elastic modulus was determined using a shaft-loaded blister test and linear and nonlinear elasticity models. Compared to net resin thin films, a 20% increase in elastic modulus was seen when 0.1 wt % MWNTs were added, suggesting MWNT alignment by spin coating. Electron microscopic observations of the fracture surfaces suggested high interfacial shear stress between MWNTs and the epoxy matrix, a result supported by both molecular mechanics simulation and micromechanics calculations.
Bispectra of Internal Tides and Parametric Subharmonic Instability
Frajka-Williams, Eleanor; MacKinnon, Jennifer A
2014-01-01
Bispectral analysis of the nonlinear resonant interaction known as parametric subharmonic instability (PSI) for a coherence semidiurnal internal tide demonstrates the ability of the bispectrum to identify and quantify the transfer rate. Assuming that the interaction is confined to a vertical plane, energy equations transform in such a way that nonlinear terms become the third-moment spectral quantity known as the bispectrum. Bispectral transfer rates computed on PSI in an idealized, fully-nonlinear, non-hydrostatic Boussinesq model compare well to model growth rates of daughter waves. Bispectra also identify the nonlinear terms responsible for energy transfer. Using resonance conditions for an M2 tide, the locus of PSI wavenumber triads is determined as a function of parent-wave frequency and wavenumbers, latitude and range of daughter-wave frequencies. The locus is used to determine the expected bispectral signal of PSI in wavenumber space. Bispectra computed using velocity profiles from the HOME experiment ...
Huberman, B A; Huberman, Bernardo A; Youssefmir, Michael
1995-01-01
Recent developments in the global liberalization of equity and currency markets, coupled to advances in trading technologies, are making markets increasingly interdependent. This increased fluidity raises questions about the stability of the international financial system. In this paper, we show that as couplings between stable markets grow, the likelihood of instabilities is increased, leading to a loss of general equilibrium as the system becomes increasingly large and diverse.
Porsezian, K.; Shafeeque Ali, A. K.; Nithyanandan, K.
2016-12-01
We theoretically investigate threshold conditions to observe modulation instability (MI) in a two-core nonlinear oppositely directed coupler (ODC) with a negative-index material (NIM) channel. Using linear stability analysis, we obtain an expression for the instability gain. The analysis shows, with two discrete instability regions, that the band at lower values of f (ratio of the backward to forward-propagating waves amplitude) is a result of the nonlinear positive index material (PIM) channel while the broader range band is a consequence of the nonlinear NIM channel. Both bands are highly sensitive to system parameters. We demonstrate that MI has a threshold-like condition in the normal dispersion regime. This study also shows that gain increases proportionally to power increases and the two instability regions approach each other, thereby narrowing the stability region. Furthermore, we report that the effect of pump power and the coupling coefficient on instability gain have an opposite relationship. Similarly, study of the influence of the nonlinear coefficient on critical power (P c ) shows that P c gradually decreases as the nonlinear coefficient increases. Thus, a comprehensive study on the influence of various physical effects on MI is reported in this paper.
Carpal instability nondissociative.
Wolfe, Scott W; Garcia-Elias, Marc; Kitay, Alison
2012-09-01
Carpal instability nondissociative (CIND) represents a spectrum of conditions characterized by kinematic dysfunction of the proximal carpal row, often associated with a clinical "clunk." CIND is manifested at the midcarpal and/or radiocarpal joints, and it is distinguished from carpal instability dissociative (CID) by the lack of disruption between bones within the same carpal row. There are four major subcategories of CIND: palmar, dorsal, combined, and adaptive. In palmar CIND, instability occurs across the entire proximal carpal row. When nonsurgical management fails, surgical options include arthroscopic thermal capsulorrhaphy, soft-tissue reconstruction, or limited radiocarpal or intercarpal fusions. In dorsal CIND, the capitate subluxates dorsally from its reduced resting position. Dorsal CIND usually responds to nonsurgical management; refractory cases respond to palmar ligament reefing and/or dorsal intercarpal capsulodesis. Combined CIND demonstrates signs of both palmar and dorsal CIND and can be treated with soft-tissue or bony procedures. In adaptive CIND, the volar carpal ligaments are slackened and are less capable of inducing the physiologic shift of the proximal carpal row from flexion into extension as the wrist ulnarly deviates. Treatment of choice is a corrective osteotomy to restore the normal volar tilt of the distal radius.
Chromosomal instability in meningiomas.
van Tilborg, Angela A G; Al Allak, Bushra; Velthuizen, Sandra C J M; de Vries, Annie; Kros, Johan M; Avezaat, Cees J J; de Klein, Annelies; Beverloo, H Berna; Zwarthoff, Ellen C
2005-04-01
Approximately 60% of sporadic meningiomas are caused by inactivation of the NF2 tumor suppressor gene on chromosome 22. No causative gene is known for the remaining 40%. Cytogenetic analysis shows that meningiomas caused by inactivation of the NF2 gene can be divided into tumors that show monosomy 22 as the sole abnormality and tumors with a more complex karyotype. Meningiomas not caused by the NF2 gene usually have a diploid karyotype. Here we report that, besides the clonal chromosomal aberrations, the chromosome numbers in many meningiomas varied from one metaphase spread to the other, a feature that is indicative of chromosomal instability. Unexpectedly and regardless of genotype, a subgroup of tumors was observed with an average number of 44.9 chromosomes and little variation in the number of chromosomes per metaphase spread. In addition, a second subgroup was recognized with a hyperdiploid number of chromosomes (average 48.5) and considerable variation in numbers per metaphase. However, this numerical instability resulted in a clonal karyotype with chromosomal gains and losses in addition to loss of chromosome 22 only in meningiomas caused by inactivation of the NF2 gene. In cultured cells of all tumor groups, bi- and multinucleated cells were seen, as well as anaphase bridges, residual chromatid strings, multiple spindle poles, and unseparated chromatids, suggesting defects in the mitotic apparatus or kinetochore. Thus, we conclude that even a benign and slow-growing tumor like a meningioma displays chromosomal instability.
Vorvolakos, Katherine; Coburn, James C; Saylor, David M
2014-04-07
An aqueous hyaluronic acid (HA(aq)) pericellular coat, when mediating the tactile aspect of cellular contact inhibition, has three tasks: interface formation, mechanical signal transmission and interface separation. To quantify the interfacial adhesive behavior of HA(aq), we induce simultaneous interface formation and separation between HA(aq) and a model hydrophobic, hysteretic Si-SAM surface. While surface tension γ remains essentially constant, interface formation and separation depend greatly on concentration (5 ≤ C ≤ 30 mg mL(-1)), molecular weight (6 ≤ MW ≤ 2000 kDa) and interfacial velocity (0 ≤ V ≤ 3 mm s(-1)), each of which affect shear elastic and loss moduli G′ and G′′, respectively. Viscoelasticity dictates the mode of interfacial motion: wetting-dewetting, capillary necking, or rolling. Wetting-dewetting is quantified using advancing and receding contact angles θ(A) and θ(R), and the hysteresis between them, yielding data landscapes for each C above the [MW, V] plane. The landscape sizes, shapes, and curvatures disclose the interplay, between surface tension and viscoelasticity, which governs interfacial dynamics. Gel point coordinates modulus G and angular frequency ω appear to predict wetting-dewetting (G 200ω0.075). Dominantly dissipative HA(aq) sticks to itself and distorts irreversibly before separating, while dominantly elastic HA(aq) makes contact and separates with only minor, reversible distortion. We propose the dimensionless number (G′V)/(ω(r)γ), varying from 10(-5) to 10(3) in this work, as a tool to predict the mode of interface formation-separation by relating interfacial kinetics with bulk viscoelasticity. Cellular contact inhibition may be thus aided or compromised by physiological or interventional shifts in [C, MW, V], and thus in (G′V)/(ω(r)γ), which affect both mechanotransduction and interfacial dynamics. These observations, understood in terms of physical properties, may be broadened to probe
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Shoulder instability; Schultergelenkinstabilitaet
Energy Technology Data Exchange (ETDEWEB)
Sailer, J.; Imhof, H. [Abteilung Osteoradiologie, Univ.-Klinik fuer Radiodiagnostik Wien (Austria)
2004-06-01
Shoulder instability is a common clinical feature leading to recurrent pain and limitated range of motion within the glenohumeral joint. Instability can be due a single traumatic event, general joint laxity or repeated episodes of microtrauma. Differentiation between traumatic and atraumatic forms of shoulder instability requires careful history and a systemic clinical examination. Shoulder laxity has to be differentiated from true instability followed by the clinical assessment of direction and degree of glenohumeral translation. Conventional radiography and CT are used for the diagnosis of bony lesions. MR imaging and MR arthrography help in the detection of soft tissue affection, especially of the glenoid labrum and the capsuloligamentous complex. The most common lesion involving the labrum is the anterior labral tear, associated with capsuloperiostal stripping (Bankart lesion). A number of variants of the Bankart lesion have been described, such as ALPSA, SLAP or HAGL lesions. The purpose of this review is to highlight different forms of shoulder instability and its associated radiological findings with a focus on MR imaging. (orig.) [German] Die Schultergelenkinstabilitaet ist haeufig fuer wiederholt auftretende Schmerzen sowie eine eingeschraenkte Beweglichkeit im Glenohumeralgelenk verantwortlich. Sie kann als Folge eines vorangegangenen Traumas, einer generellen Hyperlaxitaet oder infolge wiederholter Mikrotraumen entstehen. Die Differenzierung zwischen traumatischer und atraumatischer Form der Gelenkinstabilitaet erfordert eine sorgfaeltige Anamnese und eine genaue klinische Untersuchung. Die Gelelenklaxitaet als Differenzialdiagnose muss von der echten Instabilitaet unterschieden werden, die Instabilitaet wird dann im Rahmen des klinischen Status nach Grad und Richtung der glenohumeralen Translation unterteilt. Zur Diagnose knoecherner Laesionen werden das konventionelle Roentgen sowie die CT herangezogen. MRT sowie MR-Arthrographie dienen zur Detektion
Interfacial geometry dictates cancer cell tumorigenicity
Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.
2016-08-01
Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.
Evaluating interfacial shear stresses in composite hollo
Directory of Open Access Journals (Sweden)
Aiham Adawi
2016-09-01
Full Text Available Analytical evaluation of the interfacial shear stresses for composite hollowcore slabs with concrete topping is rare in the literature. Adawi et al. (2014 estimated the interfacial shear stiffness coefficient (ks that governs the behavior of the interface between hollowcore slabs and the concrete topping using push-off tests. This parameter is utilized in this paper to provide closed form solutions for the differential equations governing the behavior of simply supported composite hollowcore slabs. An analytical solution based on the deformation compatibility of the composite section and elastic beam theory, is developed to evaluate the shear stresses along the interface. Linear finite element modeling of the full-scale tests presented in Adawi et al. (2015 is also conducted to validate the developed analytical solution. The proposed analytical solution was found to be adequate in estimating the magnitude of horizontal shear stress in the studied composite hollowcore slabs.
Mesoscale Interfacial Dynamics in Magnetoelectric Nanocomposites
Energy Technology Data Exchange (ETDEWEB)
Shashank, Priya [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
2009-12-14
Biphasic composites are the key towards achieving enhanced magnetoelectric response. In order understand the control behavior of the composites and resultant symmetry of the multifunctional product tensors, we need to synthesized model material systems with the following features (i) interface formation through either deposition control or natural decomposition; (ii) a very high interphase-interfacial area, to maximize the ME coupling; and (iii) an equilibrium phase distribution and morphology, resulting in preferred crystallographic orientation relations between phases across the interphase-interfacial boundaries. This thought process guided the experimental evolution in this program. We initiated the research with the co-fired composites approach and then moved on to the thin film laminates deposited through the rf-magnetron sputtering and pulsed laser deposition process
Scaling for interfacial tensions near critical endpoints.
Zinn, Shun-Yong; Fisher, Michael E
2005-01-01
Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the full neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function both of temperature and of density/order parameter or chemical potential/ordering field. Accurate nonclassical critical exponents and reliable estimates for the universal amplitude ratios are included naturally on the basis of the "extended de Gennes-Fisher" local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out "manually." Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio -3.25+/-0.05 is predicted.
Interfacial transport in lithium-ion conductors
Shaofei, Wang; Liquan, Chen
2016-01-01
Physical models of ion diffusion at different interfaces are reviewed. The use of impedance spectroscopy (IS), nuclear magnetic resonance (NMR), and secondary ion mass spectrometry (SIMS) techniques are also discussed. The diffusion of ions is fundamental to the operation of lithium-ion batteries, taking place not only within the grains but also across different interfaces. Interfacial ion transport usually contributes to the majority of the resistance in lithium-ion batteries. A greater understanding of the interfacial diffusion of ions is crucial to improving battery performance. Project supported by the Beijing S&T Project, China (Grant No. Z13111000340000), the National Natural Science Foundation of China (Grant Nos. 51325206 and 11234013) and the National Basic Research Program of China (Grant No. 2012CB932900).
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Frontiers of interfacial water research :workshop report.
Energy Technology Data Exchange (ETDEWEB)
Cygan, Randall Timothy; Greathouse, Jeffery A.
2005-10-01
Water is the critical natural resource of the new century. Significant improvements in traditional water treatment processes require novel approaches based on a fundamental understanding of nanoscale and atomic interactions at interfaces between aqueous solution and materials. To better understand these critical issues and to promote an open dialog among leading international experts in water-related specialties, Sandia National Laboratories sponsored a workshop on April 24-26, 2005 in Santa Fe, New Mexico. The ''Frontiers of Interfacial Water Research Workshop'' provided attendees with a critical review of water technologies and emphasized the new advances in surface and interfacial microscopy, spectroscopy, diffraction, and computer simulation needed for the development of new materials for water treatment.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Limit Cycle Behaviour of the Bump-on-Tail Instability
DEFF Research Database (Denmark)
Janssen, P. A. E. M.; Juul Rasmussen, Jens
1981-01-01
The nonlinear dynamics of the bump‐on‐tail instability is considered. The eigenmodes have discrete k because of finite periodic boundary conditions. Increasing a critical parameter (the number density) above its neutral stable value by a small fractional amount Δ2, one mode becomes unstable....... The nonlinear dynamics of the unstable mode is determined by means of the multiple time scale method. Usually, limit cycle behavior is found. A short comparison with quasi‐linear theory is given, and the results are compared with experiment....
Microencapsulation of Chlorocyclophosphazene by Interfacial Polymerization
Institute of Scientific and Technical Information of China (English)
LIU Ya-qing; ZHAO Gui-zhe
2007-01-01
A polyurea-chlorocyclophosphazene microcapsule flame retardant is prepared by an interfacial polymerization process using 2, 4-toluene diisocyanate (TDI) and hexanediamine as the raw materials. TG tests show that the thermal decomposition temperature of chlorocyclophosphazene in microcapsule obviously rises. The flame retardancy of HDPE/chlorocyclophosphazene in microencapsules is better than that of HDPE/chlorocyclophosphazene. Mechanical properties of HDPE/chlorocyclophosphazene microencapsule turn out to be superior to those of HDPE/chlorocyclophosphazene.
Kinetics of Model Reactions for Interfacial Polymerization
Directory of Open Access Journals (Sweden)
Henry Hall
2012-02-01
Full Text Available To model the rates of interfacial polycondensations, the rates of reaction of benzoyl chloride and methyl chloroformate with various aliphatic monoamines in acetonitrile were determined at 25 °C. Buffering with picric acid slowed these extremely fast reactions so the rate constants could be determined from the rate of disappearance of picrate ion. The rates of the amine reactions correlated linearly with their Swain-Scott nucleophilicities.
Facile Interfacial Electron Transfer of Hemoglobin
Directory of Open Access Journals (Sweden)
Chunhai Fan
2005-12-01
Full Text Available Abstract: We herein describe a method of depositing hemoglobin (Hb and sulfonated polyaniline (SPAN on GC electrodes that facilitate interfacial protein electron transfer. Well-defined, reproducible, chemically reversible peaks of Hb and SPAN can be obtained in our experiments. We also observed enhanced peroxidase activity of Hb in SPAN films. These results clearly showed that SPAN worked as molecular wires and effectively exchanged electrons between Hb and electrodes.Mediated by Conjugated Polymers