WorldWideScience

Sample records for linear hydrodynamic stability

  1. The linearization method in hydrodynamical stability theory

    Yudovich, V I

    1989-01-01

    This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

  2. Hydrodynamic and hydromagnetic stability

    Chandrasekhar, S

    1981-01-01

    Dr. Chandrasekhar's book received high praise when it first appeared in 1961 as part of Oxford University Press' International Series of Monographs on Physics. Since then it has been reprinted numerous times in its expensive hardcover format. This first lower-priced, sturdy paperback edition will be welcomed by graduate physics students and scientists familiar with Dr. Chandrasekhar's work, particularly in light of the resurgence of interest in the Rayleigh-Bénard problem. This book presents a most lucid introduction to the Rayleigh-Bénard problem: it has also been applauded for its thorough, clear coverage of the theory of instabilities causing convection. Dr. Chandrasekhar considers most of the typical problems in hydromagnetic stability, with the exception of viscous shear flow; a specialized domain deserving a book unto itself. Contents include: Rotation; Stability of More General Flows; Bénard Problem; Gravitational Equilibrium and Instability; Stability of a Magnetic Field; Thermal Instability of a L...

  3. Hydrodynamic stability and stellar oscillations

    in 1961, is a standard reference on linear stability theory. It gives a ... perturbations about the equilibrium state are constants and the x, y, t dependence of the ..... anism was proposed for the formation of X-ray binaries in globular clusters. They.

  4. Numerical methods for hydrodynamic stability problems

    Fujimura, Kaoru

    1985-11-01

    Numerical methods for solving the Orr-Sommerfeld equation, which is the fundamental equation of the hydrodynamic stability theory for various shear flows, are reviewed and typical numerical results are presented. The methods of asymptotic solution, finite difference methods, initial value methods and expansions in orthogonal functions are compared. (author)

  5. Flow stabilization with active hydrodynamic cloaks.

    Urzhumov, Yaroslav A; Smith, David R

    2012-11-01

    We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder.

  6. Linearly resummed hydrodynamics in a weakly curved spacetime

    Bu, Yanyan; Lublinsky, Michael

    2015-04-01

    We extend our study of all-order linearly resummed hydrodynamics in a flat space [1, 2] to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS5 geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. [1, 2], we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. [3], the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

  7. Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

    Dubois-Boudesocque, Carine

    2000-01-01

    The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

  8. Linearly resummed hydrodynamics in a weakly curved spacetime

    Bu, Yanyan; Lublinsky, Michael

    2015-01-01

    We extend our study of all-order linearly resummed hydrodynamics in a flat space (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064) to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature N=4 super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS 5 geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid’s energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064), we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. (http://dx.doi.org/10.1103/PhysRevD.80.065026), the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

  9. Linearly resummed hydrodynamics in a weakly curved spacetime

    Bu, Yanyan; Lublinsky, Michael [Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)

    2015-04-24

    We extend our study of all-order linearly resummed hydrodynamics in a flat space (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064) to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature N=4 super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically locally AdS{sub 5} geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid’s energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs. (http://dx.doi.org/10.1103/PhysRevD.90.086003, http://dx.doi.org/10.1007/JHEP11(2014)064), we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref. (http://dx.doi.org/10.1103/PhysRevD.80.065026), the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.

  10. The hydrodynamic size of polymer stabilized nanocrystals

    Krueger, Karl M; Al-Somali, Ali M; Mejia, Michelle; Colvin, Vicki L [Department of Chemistry, Rice University, MS-60 6100 Main Street, Houston, TX 77005 (United States)

    2007-11-28

    For many emerging applications, nanocrystals are surface functionalized with polymers to control self-assembly, prevent aggregation, and promote incorporation into polymer matrices and biological systems. The hydrodynamic diameter of these nanoparticle-polymer complexes is a critical factor for many applications, and predicting this size is complicated by the fact that the structure of the grafted polymer at a nanocrystalline interface is not generally established. In this work we evaluate using size-exclusion chromatography the overall hydrodynamic diameter of nanocrystals (Au, CdSe, d<5 nm) surface coated with polystyrene of varying molecular weight. The polymer is tethered to the nanoparticles via a terminal thiol to provide strong attachment. Our data show that at full coverage the polymer assumes a brush conformation and is 44% longer than the unbound polymer in solution. The brush conformation is confirmed by comparison with models used to describe polymer brushes at flat interfaces. From this work, we suggest an empirical formula which predicts the hydrodynamic diameter of polymer coated nanoparticles based on the size of the nanoparticle core and the size of the randomly coiled unbound polymer in solution.

  11. The hydrodynamics of linear accelerations in bluegill sunfish, Lepomis macrochirus

    Wise, Tyler; Boden, Alex; Schwalbe, Margot; Tytell, Eric

    2015-11-01

    As fish swim, their body interacts with the fluid around them in order to generate thrust. In this study, we examined the hydrodynamics of linear acceleration by bluegill sunfish, Lepomis macrochirus, which swims using a carangiform mode. Carangiform swimmers primarily use their caudal fin and posterior body for propulsion, which is different from anguilliform swimmers, like eels, that undulate almost their whole body to swim. Most previous studies have examined steady swimming, but few have looked at linear accelerations, even though most fish do not often swim steadily. During steady swimming, thrust and drag forces are balanced, which makes it difficult to separate the two, but during acceleration, thrust exceeds drag, making it easier to measure; this may reveal insights into how thrust is produced. This study used particle image velocimetry (PIV) to compare the structure of the wake during steady swimming and acceleration and to estimate the axial force. Axial force increased during acceleration, but the orientation of the vortices did not differ between steady swimming and acceleration, which is different than anguilliform swimmers, whose wakes change structure during acceleration. This difference may point to fundamental differences between the two swimming modes. This material is based upon work supported by the U. S. Army Research Office under grant number W911NF-14-1-0494.

  12. Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors

    Elliott, T. S.; Majdalani, J.

    2014-11-01

    Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion.

  13. Hydrodynamic Stability Analysis of Particle-Laden Solid Rocket Motors

    Elliott, T S; Majdalani, J

    2014-01-01

    Fluid-wall interactions within solid rocket motors can result in parietal vortex shedding giving rise to hydrodynamic instabilities, or unsteady waves, that translate into pressure oscillations. The oscillations can result in vibrations observed by the rocket, rocket subsystems, or payload, which can lead to changes in flight characteristics, design failure, or other undesirable effects. For many years particles have been embedded in solid rocket propellants with the understanding that their presence increases specific impulse and suppresses fluctuations in the flowfield. This study utilizes a two dimensional framework to understand and quantify the aforementioned two-phase flowfield inside a motor case with a cylindrical grain perforation. This is accomplished through the use of linearized Navier-Stokes equations with the Stokes drag equation and application of the biglobal ansatz. Obtaining the biglobal equations for analysis requires quantification of the mean flowfield within the solid rocket motor. To that end, the extended Taylor-Culick form will be utilized to represent the gaseous phase of the mean flowfield while the self-similar form will be employed for the particle phase. Advancing the mean flowfield by quantifying the particle mass concentration with a semi-analytical solution the finalized mean flowfield is combined with the biglobal equations resulting in a system of eight partial differential equations. This system is solved using an eigensolver within the framework yielding the entire spectrum of eigenvalues, frequency and growth rate components, at once. This work will detail the parametric analysis performed to demonstrate the stabilizing and destabilizing effects of particles within solid rocket combustion

  14. Hydromagnetic thin film flow: Linear stability

    Amaouche, Mustapha; Ait Abderrahmane, Hamid; Bourdache, Lamia

    2013-01-01

    . The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while

  15. On the hydrodynamics of a solvent-satured lipid bilayer. 2. Stability criteria

    Bisch, P.M.; Wendel, H.

    1983-01-01

    The semiphenomenological model introduced recently is used to investigate the role of steric forces on the dynamics of black lipid films. A linear stability analysis of hydrodynamic fluctuations for lipid films submitted to an applyed electric field is performed. By neglecting dissipation, this our analysis is concentrated on the competitive effects of electrostatic, van der Waals and steric forces. In the long wavelenght limit it is shown that the stability of the film against bending deformations is governed by the total film tension. Similarly, for periodic thickness fluctuations the stability is determined by the film elasticity. In both cases a stabilizing positive contribution is found of steric forces produced by the overlap of lipid chains at the center of the film. The stability diagram shows a region, for sufficiently small thickness, where only bending modes are unstable. (Author) [pt

  16. Bulk hydrodynamic stability and turbulent saturation in compressing hot spots

    Davidovits, Seth; Fisch, Nathaniel J.

    2018-04-01

    For hot spots compressed at constant velocity, we give a hydrodynamic stability criterion that describes the expected energy behavior of non-radial hydrodynamic motion for different classes of trajectories (in ρR — T space). For a given compression velocity, this criterion depends on ρR, T, and d T /d (ρR ) (the trajectory slope) and applies point-wise so that the expected behavior can be determined instantaneously along the trajectory. Among the classes of trajectories are those where the hydromotion is guaranteed to decrease and those where the hydromotion is bounded by a saturated value. We calculate this saturated value and find the compression velocities for which hydromotion may be a substantial fraction of hot-spot energy at burn time. The Lindl (Phys. Plasmas 2, 3933 (1995)] "attractor" trajectory is shown to experience non-radial hydrodynamic energy that grows towards this saturated state. Comparing the saturation value with the available detailed 3D simulation results, we find that the fluctuating velocities in these simulations reach substantial fractions of the saturated value.

  17. Linear stability of tearing modes

    Cowley, S.C.; Kulsrud, R.M.; Hahm, T.S.

    1986-05-01

    This paper examines the stability of tearing modes in a sheared slab when the width of the tearing layer is much smaller than the ion Larmor radius. The ion response is nonlocal, and the quasineutrality retains its full integal form. An expansion procedure is introduced to solve the quasineutrality equation in powers of the width of the tearing layer over the ion Larmor radius. The expansion procedure is applied to the collisionless and semi-collisional tearing modes. The first order terms in the expansion we find to be strongly stabilizing. The physics of the mode and of the stabilization is discussed. Tearing modes are observed in experiments even though the slab theory predicts stability. It is proposed that these modes grow from an equilibrium with islands at the rational surfaces. If the equilibrium islands are wider than the ion Larmor radius, the mode is unstable when Δ' is positive

  18. Linear and nonlinear stability in resistive magnetohydrodynamics

    Tasso, H.

    1994-01-01

    A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its open-quotes nearnessclose quotes to necessity is analysed. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with open-quotes unconditionalclose quotes stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed. 23 refs

  19. Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas

    Yan, Wei

    2015-01-01

    We investigate the hydrodynamic theory of metals, offering systematic studies of the linear-response dynamics for an inhomogeneous electron gas. We include the quantum functional terms of the Thomas-Fermi kinetic energy, the von Weizsa¨cker kinetic energy, and the exchange-correlation Coulomb...... energies under the local density approximation. The advantages, limitations, and possible improvements of the hydrodynamic theory are transparently demonstrated. The roles of various parameters in the theory are identified. We anticipate that the hydrodynamic theory can be applied to investigate the linear...... response of complex metallic nanostructures, including quantum effects, by adjusting theory parameters appropriately....

  20. Stability problems for linear hyperbolic systems

    Eckhoff, K.S.

    1975-05-01

    The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)

  1. Hydrodynamic stability theory of double ablation front structures in inertial confinement fusion

    Yanez Vico, C.

    2012-11-01

    For moderate-Z materials, the hydrodynamic structure of the ablation region formed by the irradiation of high intensity laser beams differs from that of low-Z materials (hydrogenic ablators). In particular, the role played by the radiative energy flux becomes non-negligible for increasing atomic number material and ended up forming a second ablation front. This structure of two separated ablation fronts, called double ablation (DA) front, was confirmed in the simulations carried out by Fujioka et al. In this work a linear stability theory of DA fronts is developed for direct-drive inertial confinement fusion targets. Two models are proposed. First, a sharp boundary model where the thin front approximation is assumed for both ablation fronts. The information about the corona region that permits to close the sharp boundary model is obtained from a prior self-consistent analysis of the electronic-radiative ablation (ERA) front. Numerical results are presented as well as an analytical approach for the radiation dominated regime of very steep double ablation front structure. Second, a self-consistent numerical method where the finite length of the ablation fronts is considered. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using one-dimensional simulation results. Numerical dispersion relation is compared to the analytical sharp boundary model showing an excellent agreement for the radiation dominated regime, and the stabilization due to smooth profiles. 2D simulations are presented to validate the linear stability theory

  2. STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS

    Jorge Enrique Mayta Guillermo

    2016-12-01

    Full Text Available In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is nite. Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.

  3. Hydrodynamics of stratified epithelium: Steady state and linearized dynamics

    Yeh, Wei-Ting; Chen, Hsuan-Yi

    2016-05-01

    A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue are assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic description of tissue dynamics at the long-wavelength, long-time limit is developed, and the analysis reveals important insights into the dynamics of an epithelium close to its steady state. When the proliferative cells occupy a thin region close to the basal membrane, the relaxation rate towards the steady state is enhanced by cell division and cell apoptosis. On the other hand, when the region where proliferative cells reside becomes sufficiently thick, a flow induced by cell apoptosis close to the apical surface enhances small perturbations. This destabilizing mechanism is general for continuous self-renewal multilayered tissues; it could be related to the origin of certain tissue morphology, tumor growth, and the development pattern.

  4. Linear ideal MHD stability calculations for ITER

    Hogan, J.T.

    1988-01-01

    A survey of MHD stability limits has been made to address issues arising from the MHD--poloidal field design task of the US ITER project. This is a summary report on the results obtained to date. The study evaluates the dependence of ballooning, Mercier and low-n ideal linear MHD stability on key system parameters to estimate overall MHD constraints for ITER. 17 refs., 27 figs

  5. Linear stability analysis of supersonic axisymmetric jets

    Zhenhua Wan

    2014-01-01

    Full Text Available Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory (LST. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.

  6. Stability analysis and stabilization strategies for linear supply chains

    Nagatani, Takashi; Helbing, Dirk

    2004-04-01

    Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as “bull-whip effect”. Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon τ is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.

  7. Linear stability analysis of heated parallel channels

    Nourbakhsh, H.P.; Isbin, H.S.

    1982-01-01

    An analyis is presented of thermal hydraulic stability of flow in parallel channels covering the range from inlet subcooling to exit superheat. The model is based on a one-dimensional drift velocity formulation of the two phase flow conservation equations. The system of equations is linearized by assuming small disturbances about the steady state. The dynamic response of the system to an inlet flow perturbation is derived yielding the characteristic equation which predicts the onset of instabilities. A specific application is carried out for homogeneous and regional uniformly heated systems. The particular case of equal characteristic frequencies of two-phase and single phase vapor region is studied in detail. The D-partition method and the Mikhailov stability criterion are used for determining the marginal stability boundary. Stability predictions from the present analysis are compared with the experimental data from the solar test facility. 8 references

  8. Analysis of the hydrodynamic stability of natural circulation

    Olive, J.; Baby, J.P.

    1980-01-01

    A mathematical model (EOLE) for the analysis of the stability of boilers with natural circulation is discussed. The method employed consists in linearizing one-dimensional flow equations and in integrating them while employing the Laplace transformation. The properties of a two-phase fluid are schematized by a homogeneous model with slip. The computation results in the circulation loop transfer functions and its natural modes of oscillation (frequency and damping). A discussion follows which compares results obtained with this method to those of other existing models in the case of a straight pipe with forced circulation. Agreement proved to be satisfactory. The results are then given of a parametric study involving the stability of a PWR natural circulation steam generator. These results show that the model can satisfy, at least qualitatively, trends observed empirically or obtained with other more complex theoretical models. (author)

  9. Quantifying Stability in Complex Networks: From Linear to Basin Stability

    Kurths, Jürgen

    The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. Specifically, we employ a component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends. Further, we analyse the particular function of certain network motifs to promote the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design. Moreover, it will be shown that basin stability enables uncovering the mechanism for explosive synchronization and

  10. Linear inductive voltage adders (IVA) for advanced hydrodynamic radiography

    Mazarakis, M.G.; Boyes, J.D.; Johnson, D.L.

    1998-01-01

    The electron beam which drifts through the multiple cavities of conventional induction linacs (LIA) is replaced in an IVA by a cylindrical metal conductor which extends along the entire length of the device and effectuates the addition of the accelerator cavity voltages. In the approach to radiography, the linear inductive voltage adder drives a magnetically immersed electron diode with a millimeter diameter cathode electrode and a planar anode/bremsstrahlung converter. Both anode and cathode electrodes are immersed in a strong (15--50 T) solenoidal magnetic field. The electron beam cross section is approximately of the same size as the cathode needle and generates a similar size, very intense x-ray beam when it strikes the anode converter. An IVA driven diode can produce electron beams of equal size and energy as a LIA but with much higher currents (40--50 kA versus 4--5 kA), simpler hardware and thus lower cost. The authors present here first experimental validations of the technology utilizing HERMES 3 and SABRE IVA accelerators. The electron beam voltage and current were respectively of the order of 10 MV and 40 kA. X-ray doses of up to 1 kR at sign 1 m and spot sizes as small as 1.7 mm (at 200 R doses) were measured

  11. Hydrodynamic of a deformed bubble in linear shear flow

    Adoua, S.R.

    2007-07-01

    This work is devoted to the study of an oblate spheroidal bubble of prescribed shape set fixed in a linear shear flow using direct numerical simulation. The three dimensional Navier-Stokes equations are solved in orthogonal curvilinear coordinates using a finite volume method. The bubble response is studied over a wide range of the aspect ratio (1-2.7), the bubble Reynolds number (50-2000) and the non-dimensional shear rate (0.-1.2). The numerical simulations shows that the shear flow imposes a plane symmetry of the wake whatever the parameters of the flow. The trailing vorticity is organized into two anti-symmetrical counter rotating tubes with a sign imposed by the competition of two mechanisms (the Lighthill mechanism and the instability of the wake). Whatever the Reynolds number, the lift coefficient reaches the analytical value obtained in an inviscid, weakly sheared flow corresponding to a lift force oriented in the same direction as that of a spherical bubble. For moderate Reynolds numbers, the direction of the lift force reverses when the bubble aspect ratio is large enough as observed in experiments. This reversal occurs for aspect ratios larger than 2.225 and is found to be directly linked to the sign of the trailing vorticity which is concentrated within two counter-rotating threads which propel the bubble in a direction depending of their sign of rotation. The behavior of the drag does not revel any significant effect induced by the wake structure and follows a quadratic increase with the shear rate. Finally, the torque experienced by the bubble also reverses for the same conditions inducing the reversal of the lift force. By varying the orientation of the bubble in the shear flow, a stable equilibrium position is found corresponding to a weak angle between the small axis of the bubble and the flow direction. (author)

  12. Airfoil stall interpreted through linear stability analysis

    Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis

    2017-11-01

    Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.

  13. New linear theory of hydrodynamic instability of the Hagen-Poiseuille flow and the blood swirling flows formation

    Sergey G. Chefranov

    2012-11-01

    Full Text Available Aims This paper deals with solving of a century-old paradox of linear stability for the Hagen-Poiseuille flow. A new mechanism of dissipative hydrodynamic instability has been established herein, and a basis for the forming of helical structural organization of bloodstream and respective energy effectiveness of the cardiovascular system functioning has been defined by the authors. Materials and methods Theory of hydrodynamic instability, Galerkin’s approximation. Results A new condition Re > Reth-min ≈ 124 of linear (exponential instability of the Hagen-Poisseuille (HP flow with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. The disturbances necessarily shall have quasi-periodic longitudinal variability along the pipe axis that corresponds to the observed data. Conclusion We show that the obtained estimate of value of Reth-min corresponds to the condition of independence of the main result (on the linear instability of the HP flow when Re > Reth-min from the procedure of averaging used in the Galerkin approximation. Thus, we obtain the possible natural mechanism for the blood swirling flows formations observed in the aorta and the large blood vessels.

  14. Linear stability of microtearing modes in ASDEX

    Giannone, L.

    1987-12-01

    The linear stability of microtearing modes in typical ASDEX discharges have been calculated. In the case of Ohmic discharges it was found that unstable modes are predicted to be located towards the centre of the plasma. For L and H discharges the zone of instability shifts towards the plasma edge. The interpretation of an increase or decrease in the amplitude of broadband magnetic fluctuations during L and H discharges must be interpreted with caution, since the amplitude observed is strongly dependent on the radial position of the instability. (orig./GG)

  15. Decoherence of histories and hydrodynamic equations for a linear oscillator chain

    Halliwell, J.J.

    2003-01-01

    We investigate the decoherence of histories of local densities for linear oscillators models. It is shown that histories of local number, momentum and energy density are approximately decoherent, when coarse grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally induced decoherence. We discuss the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities

  16. Integrability and Linear Stability of Nonlinear Waves

    Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

    2018-03-01

    It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

  17. Laboratory Study of Magnetorotational Instability and Hydrodynamic Stability at Large Reynolds Numbers

    Ji, H.; Burin, M.; Schartman, E.; Goodman, J.; Liu, W.

    2006-01-01

    Two plausible mechanisms have been proposed to explain rapid angular momentum transport during accretion processes in astrophysical disks: nonlinear hydrodynamic instabilities and magnetorotational instability (MRI). A laboratory experiment in a short Taylor-Couette flow geometry has been constructed in Princeton to study both mechanisms, with novel features for better controls of the boundary-driven secondary flows (Ekman circulation). Initial results on hydrodynamic stability have shown negligible angular momentum transport in Keplerian-like flows with Reynolds numbers approaching one million, casting strong doubt on the viability of nonlinear hydrodynamic instability as a source for accretion disk turbulence.

  18. Numerical stability in problems of linear algebra.

    Babuska, I.

    1972-01-01

    Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

  19. Rippled shock front solutions for testing hydrodynamic stability simulations

    Munro, D.H.

    1989-01-01

    The response of a shock front to arbitrary small perturbations can be calculated analytically. Such rippled shock front solutions are useful for determining the accuracy of hydrodynamic simulation codes such as LASNEX [Comments Plasma Phys. Controlled Fusion 2, 51 (1977)], which are used to compute perturbation growth in inertial fusion targets. The LASNEX fractional errors are of order κ 2 L 2 , where κ is the transverse wavenumber of the perturbation, and L is the largest zone dimension. Numerical errors are about 25% for a calculation using 26 zones per transverse wavelength

  20. Hydromagnetic thin film flow: Linear stability

    Amaouche, Mustapha

    2013-08-30

    This paper deals with the long wave instability of an electroconductor fluid film, flowing down an inclined plane at small to moderate Reynolds numbers, under the action of electromagnetic fields. A coherent second order long wave model and two simplified versions of it, referred to as first and second reduced models (FRM and SRM), are proposed to describe the nonlinear behavior of the flow. The modeling procedure consists of a combination of the lubrication theory and the weighted residual approach using an appropriate projection basis. A suitable choice of weighting functions allows a significant reduction of the dimension of the problem. The full model is naturally unique, i.e., independent of the particular form of the trial functions. The linear stability of the problem is investigated, and the influence of electromagnetic field on the flow stability is analyzed. Two cases are considered: the applied magnetic field is either normal or parallel to the fluid flow direction, while the electric field is transversal. The numerical solution of the Orr-Sommerfeld (OS) eigenvalue problem and those of the depth averaging model are used to assess the accuracy of the reduced models. It is found that the current models have the advantage of the Benney-like model, which is known to asymptote the exact solution near criticality. Moreover, far from the instability threshold, the current reduced models continue to follow the OS solution up to moderate Reynolds numbers, while the averaging model diverges rapidly. The model SRM gives better results than FRM beyond sufficiently high Reynolds numbers.

  1. Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance

    Baldwin, C.; Brown, P.N.; Falgout, R.; Graziani, F.; Jones, J.

    1999-01-01

    Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. The authors present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation-hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5--6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. They perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1,000 to 100,000 zones. The fundamental question they address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? They find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), they see speedups in CPU time of factors of ∼15--30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient

  2. How (non-)linear is the hydrodynamics of heavy ion collisions?

    Floerchinger, Stefan; Wiedemann, Urs Achim [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Beraudo, Andrea [Physics Department, Theory Unit, CERN, CH-1211 Genève 23 (Switzerland); Dep. de Fisica de Particulas, U. de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain); Del Zanna, Luca [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze (Italy); Inghirami, Gabriele [Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze) (Italy); Rolando, Valentina [INFN - Sezione di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy); Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44100 Ferrara (Italy)

    2014-07-30

    We provide evidence from full numerical solutions that the hydrodynamical evolution of initial density fluctuations in heavy ion collisions can be understood order-by-order in a perturbative series in deviations from a smooth and azimuthally symmetric background solution. To leading linear order, modes with different azimuthal wave numbers do not mix. When quadratic and higher order corrections are numerically sizable, they can be understood as overtones with corresponding wave numbers in a perturbative series. Several findings reported in the recent literature result naturally from the general perturbative series formulated here.

  3. Two-component fluid membranes near repulsive walls: Linearized hydrodynamics of equilibrium and nonequilibrium states.

    Sankararaman, Sumithra; Menon, Gautam I; Sunil Kumar, P B

    2002-09-01

    We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, using a model that incorporates curvature-concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al., Phys. Rev. E 64, 021908 (2001)] for nonequilibrium force centers embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid egg phosphatidyl choline (EPC) bilayers. The pump-membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. These results should apply, more generally, to equilibrium fluid membranes comprised of two components, in which the effects of curvature-concentration coupling are significant, above the threshold for phase separation. We then discuss the fluctuations and mode structure in the steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly nonequilibrium result is a consequence of the incorporation of curvature-concentration coupling in our hydrodynamic treatment. This result also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls upon neglecting the role played by such couplings may need to be reevaluated.

  4. Stability of Linear Equations--Algebraic Approach

    Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

    2012-01-01

    This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

  5. Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

    Gao, Song

    2013-05-01

    The Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities. Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase. In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields.

  6. Hydrodynamic stability of inverted annular flow in an adiabatic simulation

    De Jarlais, G.; Ishii, M.; Linehan, J.

    1986-01-01

    Inverted annular flow was simulated adiabatically with turbulent water jets, issuing downward from large aspect ratio nozzles, enclosed in gas annuli. Velocities, diameters, and gas species were varied, and core jet length, shape, breakup mode, and dispersed core droplet sizes were recorded at approximately 750 data points. Inverted annular flow destabilization led to inverted slug flow at low relative velocities, and to dispersed droplet flow, core breakup length correlations were developed by extending work on free liquid jets to include this coaxial, jet disintegration phenomenon. The results show length dependence upon D/sub J/, Re/sub J/, We/sub J/, α, and We/sub G/,rel. Correlations for core shape, breakup mechanisms, and dispersed core droplet size were also developed, by extending the results of free jet stability, roll wave entrainment, and churn turbulent droplet stability studies

  7. Linear and nonlinear stability analysis, associated to experimental fast reactors

    Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

    1980-07-01

    Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt

  8. Weakly sheared active suspensions: hydrodynamics, stability, and rheology.

    Cui, Zhenlu

    2011-03-01

    We present a kinetic model for flowing active suspensions and analyze the behavior of a suspension subjected to a weak steady shear. Asymptotic solutions are sought in Deborah number expansions. At the leading order, we explore the steady states and perform their stability analysis. We predict the rheology of active systems including an activity thickening or thinning behavior of the apparent viscosity and a negative apparent viscosity depending on the particle type, flow alignment, and the anchoring conditions, which can be tested on bacterial suspensions. We find remarkable dualities that show that flow-aligning rodlike contractile (extensile) particles are dynamically and rheologically equivalent to flow-aligning discoid extensile (contractile) particles for both tangential and homeotropic anchoring conditions. Another key prediction of this work is the role of the concentration of active suspensions in controlling the rheological behavior: the apparent viscosity may decrease with the increase of the concentration.

  9. Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

    Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

    2011-03-21

    We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

  10. Stability and response bounds of non-conservative linear systems

    Pommer, Christian

    2003-01-01

    For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...

  11. Periodic feedback stabilization for linear periodic evolution equations

    Wang, Gengsheng

    2016-01-01

    This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

  12. Decentralized linear quadratic power system stabilizers for multi ...

    Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.

  13. Strong-stability-preserving additive linear multistep methods

    Hadjimichael, Yiannis; Ketcheson, David I.

    2018-01-01

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed

  14. Stability and stabilization of linear systems with saturating actuators

    Tarbouriech, Sophie; Gomes da Silva Jr, João Manoel; Queinnec, Isabelle

    2011-01-01

    Gives the reader an in-depth understanding of the phenomena caused by the more-or-less ubiquitous problem of actuator saturation. Proposes methods and algorithms designed to avoid, manage or overcome the effects of actuator saturation. Uses a state-space approach to ensure local and global stability of the systems considered. Compilation of fifteen years' worth of research results.

  15. Nonparallel linear stability analysis of unconfined vortices

    Herrada, M. A.; Barrero, A.

    2004-10-01

    Parabolized stability equations [F. P. Bertolotti, Th. Herbert, and P. R. Spalart, J. Fluid. Mech. 242, 441 (1992)] have been used to study the stability of a family of swirling jets at high Reynolds numbers whose velocity and pressure fields decay far from the axis as rm-2 and r2(m-2), respectively [M. Pérez-Saborid, M. A. Herrada, A. Gómez-Barea, and A. Barrero, J. Fluid. Mech. 471, 51 (2002)]; r is the radial distance and m is a real number in the interval 0

  16. Linear waves and stability in ideal magnetohydrodynamics

    Eckhoff, K.S.

    1987-05-01

    Linear waves superimposed on an arbitrary basic state in ideal magnetohydrodynamics are studied by an asymptotic expansion valid for short wavelenghts. The theory allows for a gravitational potential, and it may therefore be applied both in astrophysics and in problems related to thermonuclear fusion. The linearized equations for the perturbations of the basic state are found in the form of a symmetric hyperbolic system. This symmetric hyperbolic system is shown to possess characteristics of nonuniform multiplicity, which implies that waves of different types may interact. In particular it is shown that the mass waves, the Alf-n waves, and the slow magnetoacoustic waves will persistently interact in the exceptional case where the local wave number vector is perpendicular to the magnetic field. The equations describing this interaction are found in the form of a weakly coupled hyperbolic system. This weakly coupled hyperbloc system is studied in a number of special cases, and detailed analytic results are obtained for some such cases. The results show that the interaction of the waves may be one of the major causes of instability of the basic state. It seems beyond doubt that the interacting waves contain the physically relevant parts of the waves, which often are referred to as ballooning modes, including Suydam modes and Mercier modes

  17. ON THE STABILIZATION OF THE LINEAR HYBRID SYSTEM STRUCTURE

    Kirillov

    2014-11-01

    Full Text Available The linear control hybrid system, consisting of a fi- nite set of subsystems (modes having different dimensions, is considered. The moments of reset time are determined by some complementary function – evolutionary time. This function satisfies the special complementary ordinary differential equation. The mode stabilization problem is solved for some class of piecewise linear controls. The method of stabilization relies on the set of invariant planes, the existence of which is due to the special form of the hybrid system.

  18. Impact of finite rate chemistry on the hydrodynamic stability of shear flows in turbulent lean premixed combustion

    Dagan, Yuval; Ghoniem, Ahmed

    2017-11-01

    Recent experimental observations show that the dynamic response of a reactive flow is strongly impacted by the fuel chemistry. In order to gain insight into some of the underlying mechanisms we formulate a new linear stability model that incorporates the impact of finite rate chemistry on the hydrodynamic stability of shear flows. Contrary to previous studies which typically assume that the velocity field is independent of the kinetic rates, the velocity field in our study is coupled with the temperature field. Using this formulation, we reproduce previous results, e.g., most unstable global modes, obtained for non-reacting shear flow. Moreover, we show that these modes are significantly altered in frequency and gain by the presence of a reaction region within the shear layer. This qualitatively agrees with results of our recent experimental and numerical studies, which show that the flame surface location relative to the shear layer influences the stability characteristics in combustion tunnels. This study suggests a physical explanation for the observed impact of finite rate chemistry on shear flow stability.

  19. Decentralized linear quadratic power system stabilizers for multi ...

    Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

  20. Mathematical modelling and linear stability analysis of laser fusion cutting

    Hermanns, Torsten; Schulz, Wolfgang; Vossen, Georg; Thombansen, Ulrich

    2016-01-01

    A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

  1. Mathematical modelling and linear stability analysis of laser fusion cutting

    Hermanns, Torsten; Schulz, Wolfgang [RWTH Aachen University, Chair for Nonlinear Dynamics, Steinbachstr. 15, 52047 Aachen (Germany); Vossen, Georg [Niederrhein University of Applied Sciences, Chair for Applied Mathematics and Numerical Simulations, Reinarzstr.. 49, 47805 Krefeld (Germany); Thombansen, Ulrich [RWTH Aachen University, Chair for Laser Technology, Steinbachstr. 15, 52047 Aachen (Germany)

    2016-06-08

    A model for laser fusion cutting is presented and investigated by linear stability analysis in order to study the tendency for dynamic behavior and subsequent ripple formation. The result is a so called stability function that describes the correlation of the setting values of the process and the process’ amount of dynamic behavior.

  2. [Study on retention and stability of linear occlusal complete dentures].

    Zhang, Ping; Xu, Jun

    2003-01-01

    To learn retention and stability of linear occlusal complete dentures by investigating the subjective feelings of patient and the value of retention force. Static retention forces of maxillary and mandibular dentures were measured for 25 patients wearing linear occlusal dentures by using Hz-1 retention dynamometer. The subjective feelings of patients in functional state were gained simultaneously through questionnaire. Linear occlusal dentures demonstrate good retention in static and dynamic state. Among patients with severe resorption of residual ridge (RRR), mandibular linear occlusal dentures (shown good retentive subjective feelings) demonstrate significantly smaller retention force than those with slight or medium degree of RRR. There is no correlation between the subjective feelings and the values of retention forces of mandibular dentures. The subjective feelings of patients wearing new linear occlusal dentures are much better than that of old anatomic occlusal dentures. Linear occlusal dentures improve the performances of dentures by enhancing their stability during mastication movement.

  3. Linear stability analysis in a solid-propellant rocket motor

    Kim, K.M.; Kang, K.T.; Yoon, J.K. [Agency for Defense Development, Taejon (Korea, Republic of)

    1995-10-01

    Combustion instability in solid-propellant rocket motors depends on the balance between acoustic energy gains and losses of the system. The objective of this paper is to demonstrate the capability of the program which predicts the standard longitudinal stability using acoustic modes based on linear stability analysis and T-burner test results of propellants. Commercial ANSYS 5.0A program can be used to calculate the acoustic characteristic of a rocket motor. The linear stability prediction was compared with the static firing test results of rocket motors. (author). 11 refs., 17 figs.

  4. On the stability of non-linear systems

    Guelman, M.

    1968-09-01

    A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr

  5. Comment on ``Attractive forces between ions in quantum plasmas: Failure of linearized quantum hydrodynamics''

    Shukla, P. K.; Eliasson, B.; Akbari-Moghanjoughi, M.

    2013-03-01

    In a recent paper, Bonitz, Pehlke, and Schoof [Phys. Rev. E10.1103/PhysRevE.87.033105 87, 033105 (2013)], hereafter referred to as BPS, have raised some points against the Shukla-Eliasson attractive potential [P. K. Shukla and B. Eliasson, Phys. Rev. Lett.0031-900710.1103/PhysRevLett.108.165007 108, 165007 (2012); P. K. Shukla and B. Eliasson, Phys. Rev. Lett.0031-900710.1103/PhysRevLett.108.219902 108, 219902(E) (2012); P. K. Shukla and B. Eliasson, Phys. Rev. Lett.10.1103/PhysRevLett.109.019901 109, 019901(E) (2012)], hereafter referred to as SEAP, around a stationary test charge in a quantum plasma. Our objective here is to discuss the insufficiency of the BPS reasoning concerning the applicability of the linearized quantum hydrodynamic theory, as well as to point out the shortcomings in BPS’s arguments and to suggest how to salvage BPS’s density functional theory and simulations, which have failed to produce results that correctly match with that of Shukla and Eliasson.

  6. Hydrodynamic interaction of two particles in confined linear shear flow at finite Reynolds number

    Yan, Yiguang; Morris, Jeffrey F.; Koplik, Joel

    2007-11-01

    We discuss the hydrodynamic interactions of two solid bodies placed in linear shear flow between parallel plane walls in a periodic geometry at finite Reynolds number. The computations are based on the lattice Boltzmann method for particulate flow, validated here by comparison to previous results for a single particle. Most of our results pertain to cylinders in two dimensions but some examples are given for spheres in three dimensions. Either one mobile and one fixed particle or else two mobile particles are studied. The motion of a mobile particle is qualitatively similar in both cases at early times, exhibiting either trajectory reversal or bypass, depending upon the initial vector separation of the pair. At longer times, if a mobile particle does not approach a periodic image of the second, its trajectory tends to a stable limit point on the symmetry axis. The effect of interactions with periodic images is to produce nonconstant asymptotic long-time trajectories. For one free particle interacting with a fixed second particle within the unit cell, the free particle may either move to a fixed point or take up a limit cycle. Pairs of mobile particles starting from symmetric initial conditions are shown to asymptotically reach either fixed points, or mirror image limit cycles within the unit cell, or to bypass one another (and periodic images) indefinitely on a streamwise periodic trajectory. The limit cycle possibility requires finite Reynolds number and arises as a consequence of streamwise periodicity when the system length is sufficiently short.

  7. Surf Zone Hydrodynamics and its Utilization in Biotechnical Stabilization of Water Reservoir Banks

    Petr Pelikán

    2014-01-01

    Full Text Available The water reservoir banks are eroded mainly by two factors. The first one is wave action (i.e. wave abrasion affecting the bank in direction from the reservoir. The second one is the influence of water flowing downward over the bank surface in direction from land into the reservoir (e.g. rainfall. The determination of regular altitudinal emplacement of proper designed particular biotechnical stabilization elements is the most important factor on which the right functionality of whole construction depends. Surf zone hydrodynamics solves the wave and water level changes inside the region extending from the wave breaking point to the limit of wave up-rush. The paper is focused on the utilization of piece of knowledge from a part of sea coast hydrodynamics and new approach in its application in the conditions of inland water bodies when designing the biotechnical stabilization elements along the shorelines. The “reinforced grass carpets” as a type of biotechnical method of bank stabilization are presented in the paper; whether the growth of grass root system is dependent on presence or absence of geomats in the soil structure and proceeding of their establishment on the shorelines.

  8. Hydrodynamic-driven stability analysis of morphological patterns on stalactites and implications for cave paleoflow reconstructions.

    Camporeale, Carlo; Ridolfi, Luca

    2012-06-08

    A novel hydrodynamic-driven stability analysis is presented for surface patterns on speleothems, i.e., secondary sedimentary cave deposits, by coupling fluid dynamics to the geochemistry of calcite precipitation or dissolution. Falling film theory provides the solution for the flow-field and depth perturbations, the latter being crucial to triggering patterns known as crenulations. In a wide range of Reynolds numbers, the model provides the dominant wavelengths and pattern celerities, in fair agreement with field data. The analysis of the phase velocity of ridges on speleothems has a potential as a proxy of past film flow rates, thus suggesting a new support for paleoclimate analyses.

  9. Flow Hydrodynamics across Open Channel Flows with Riparian Zones: Implications for Riverbank Stability

    Da Liu

    2017-09-01

    Full Text Available Riverbank vegetation is of high importance both for preserving the form (morphology and function (ecology of natural river systems. Revegetation of riverbanks is commonly used as a means of stream rehabilitation and management of bank instability and erosion. In this experimental study, the effect of different riverbank vegetation densities on flow hydrodynamics across the channel, including the riparian zone, are reported and discussed. The configuration of vegetation elements follows either linear or staggered arrangements as vegetation density is progressively increased, within a representative range of vegetation densities found in nature. Hydrodynamic measurements including mean streamwise velocity and turbulent intensity flow profiles are recorded via acoustic Doppler velocimetry (ADV—both at the main channel and within the riverbank. These results show that for the main channel and the toe of riverbank, turbulence intensity for the low densities (λ ≈ 0 to 0.12 m−1 can increase up to 40% compared the case of high densities (λ = 0.94 to 1.9 m−1. Further analysis of these data allowed the estimation of bed-shear stresses, demonstrating 86% and 71% increase at the main channel and near the toe region, for increasing densities (λ = 0 to 1.9 m−1. Quantifying these hydrodynamic effects is important for assessing the contribution of physically representative ranges of riparian vegetation densities on hydrogeomorphologic feedback.

  10. Non linear stability analysis of parallel channels with natural circulation

    Mishra, Ashish Mani; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in

    2016-12-01

    Highlights: • Nonlinear instabilities in natural circulation loop are studied. • Generalized Hopf points, Sub and Supercritical Hopf bifurcations are identified. • Bogdanov–Taken Point (BT Point) is observed by nonlinear stability analysis. • Effect of parameters on stability of system is studied. - Abstract: Linear stability analysis of two-phase flow in natural circulation loop is quite extensively studied by many researchers in past few years. It can be noted that linear stability analysis is limited to the small perturbations only. It is pointed out that such systems typically undergo Hopf bifurcation. If the Hopf bifurcation is subcritical, then for relatively large perturbation, the system has unstable limit cycles in the (linearly) stable region in the parameter space. Hence, linear stability analysis capturing only infinitesimally small perturbations is not sufficient. In this paper, bifurcation analysis is carried out to capture the non-linear instability of the dynamical system and both subcritical and supercritical bifurcations are observed. The regions in the parameter space for which subcritical and supercritical bifurcations exist are identified. These regions are verified by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver.

  11. Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

    Moawad, S. M.; Moawad

    2013-10-01

    The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

  12. Relevance of Linear Stability Results to Enhanced Oil Recovery

    Ding, Xueru; Daripa, Prabir

    2012-11-01

    How relevant can the results based on linear stability theory for any problem for that matter be to full scale simulation results? Put it differently, is the optimal design of a system based on linear stability results is optimal or even near optimal for the complex nonlinear system with certain objectives of interest in mind? We will address these issues in the context of enhanced oil recovery by chemical flooding. This will be based on an ongoing work. Supported by Qatar National Research Fund (a member of the Qatar Foundation).

  13. Stability analysis of linear switching systems with time delays

    Li Ping; Zhong Shouming; Cui Jinzhong

    2009-01-01

    The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.

  14. An active interferometer-stabilization scheme with linear phase control

    Andresen, Esben Ravn; Krishnamachari, v v; Potma, E O

    2006-01-01

    We report a simple and robust computer-based active interferometer stabilization scheme which does not require modulation of the interfering beams and relies on an error signal which is linearly related to the optical path difference. In this setup, a non-collinearly propagating reference laser...... beam stabilizes the interference output of the laser light propagating collinearly through the interferometer. This stabilization scheme enables adjustable phase control with 20 ms switching times in the range from 0.02π radians to 6π radians at 632.8 nm....

  15. Strong-stability-preserving additive linear multistep methods

    Hadjimichael, Yiannis

    2018-02-20

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain larger monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding nonadditive SSP linear multistep methods.

  16. Linear local stability of electrostatic drift modes in helical systems

    Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.

    2003-01-01

    We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)

  17. Stability analysis of switched linear systems defined by graphs

    Athanasopoulos, N.; Lazar, M.

    2014-01-01

    We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,

  18. Stability Analysis for Multi-Parameter Linear Periodic Systems

    Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli

    1999-01-01

    This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...

  19. Criteria for stability of linear dynamical systems with multiple delays ...

    In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the ...

  20. On the calculation of linear stability with the aid of asymptotic solutions of Orr-Sommerfeld equation, 1

    Fujimura, Kaoru

    1980-11-01

    The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III 1 ) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)

  1. Three caveats for linear stability theory: Rayleigh-Benard convection

    Greenside, H.S.

    1984-06-01

    Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

  2. Stability of non-linear constitutive formulations for viscoelastic fluids

    Siginer, Dennis A

    2014-01-01

    Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.

  3. Strong practical stability and stabilization of uncertain discrete linear repetitive processes

    Dabkowski, Pavel; Galkowski, K.; Bachelier, O.; Rogers, E.; Kummert, A.; Lam, J.

    2013-01-01

    Roč. 20, č. 2 (2013), s. 220-233 ISSN 1070-5325 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : strong practical stability * stabilization * uncertain discrete linear repetitive processes * linear matrix inequality Subject RIV: BC - Control Systems Theory Impact factor: 1.424, year: 2013 http://onlinelibrary.wiley.com/doi/10.1002/nla.812/abstract

  4. Microscopic model for the non-linear fluctuating hydrodynamic of 4 He superfluid helium deduced by maximum entropy method

    Alvarez R, J.T.

    1998-01-01

    This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix

  5. A Non-Linear Digital Computer Model Requiring Short Computation Time for Studies Concerning the Hydrodynamics of the BWR

    Reisch, F; Vayssier, G

    1969-05-15

    This non-linear model serves as one of the blocks in a series of codes to study the transient behaviour of BWR or PWR type reactors. This program is intended to be the hydrodynamic part of the BWR core representation or the hydrodynamic part of the PWR heat exchanger secondary side representation. The equations have been prepared for the CSMP digital simulation language. By using the most suitable integration routine available, the ratio of simulation time to real time is about one on an IBM 360/75 digital computer. Use of the slightly different language DSL/40 on an IBM 7044 computer takes about four times longer. The code has been tested against the Eindhoven loop with satisfactory agreement.

  6. On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability

    Janke, Erik; Balakumar, Ponnampalam

    1999-01-01

    The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.

  7. Linear and nonlinear kinetic-stability studies in tokamaks

    Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.

    1982-09-01

    This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities

  8. Linear Stability of Binary Alloy Solidification for Unsteady Growth Rates

    Mazuruk, K.; Volz, M. P.

    2010-01-01

    An extension of the Mullins and Sekerka (MS) linear stability analysis to the unsteady growth rate case is considered for dilute binary alloys. In particular, the stability of the planar interface during the initial solidification transient is studied in detail numerically. The rapid solidification case, when the system is traversing through the unstable region defined by the MS criterion, has also been treated. It has been observed that the onset of instability is quite accurately defined by the "quasi-stationary MS criterion", when the growth rate and other process parameters are taken as constants at a particular time of the growth process. A singular behavior of the governing equations for the perturbed quantities at the constitutional supercooling demarcation line has been observed. However, when the solidification process, during its transient, crosses this demarcation line, a planar interface is stable according to the linear analysis performed.

  9. Stability analysis of switched linear systems defined by graphs

    Athanasopoulos, Nikolaos; Lazar, Mircea

    2015-01-01

    We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...

  10. Linear Quantum Systems: Non-Classical States and Robust Stability

    2016-06-29

    modulation and entanglement in a compound gradient echo memory, Physical Review A 93(2) 023809 2016. We present a theoretical model for a Kerr...Carvalho, M. Hedges and M R James, Analysis of the operation of gradient echo memories using a quantum input-output model, New Journal of Physics , 15...new structured uncertainty methods that ensure robust stability of quantum systems based on nominal linear models, and (v) physical realizability

  11. On Numerical Stability in Large Scale Linear Algebraic Computations

    Strakoš, Zdeněk; Liesen, J.

    2005-01-01

    Roč. 85, č. 5 (2005), s. 307-325 ISSN 0044-2267 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear algebraic systems * eigenvalue problems * convergence * numerical stability * backward error * accuracy * Lanczos method * conjugate gradient method * GMRES method Subject RIV: BA - General Mathematics Impact factor: 0.351, year: 2005

  12. Linear Dimensional Stability of Irreversible Hydrocolloid Materials Over Time.

    Garrofé, Analía B; Ferrari, Beatriz A; Picca, Mariana; Kaplan, Andrea E

    2015-12-01

    The aim of this study was to evaluate the linear dimensional stability of different irreversible hydrocolloid materials over time. A metal mold was designed with custom trays made of thermoplastic sheets (Sabilex, sheets 0.125 mm thick). Perforations were made in order to improve retention of the material. Five impressions were taken with each of the following: Kromopan 100 (LASCOD) [AlKr], which has dimensional stability of 100 hours, and Phase Plus (ZHERMACK) [AlPh], which has dimensional stability of 48 hours. Standardized digital photographs were taken at different time intervals (0, 15, 30, 45, 60, 120 minutes; 12, 24 and 96 hours), using an "ad-hoc" device. The images were analyzed with software (UTHSCSA Image Tool) by measuring the distance between intersection of the lines previously made at the top of the mold. The results were analyzed by ANOVA for repeated measures. Initial and final values were (mean and standard deviation): AlKr: 16.44 (0.22) and 16.34 (0.11), AlPh: 16.40 (0.06) and 16.18 (0.06). Statistical evaluation showed significant effect of material and time factors. Under the conditions in this study, time significantly affects the linear dimensional stability of irreversible hydrocolloid materials. Sociedad Argentina de Investigación Odontológica.

  13. Hydrodynamic stability of thermoviscous liquid film inside a rotating horizontal cylinder: Heating and cooling effects

    Kumawat, Tara Chand; Tiwari, Naveen

    2018-03-01

    Steady two-dimensional solutions and their stability analysis are presented for thin film of a thermoviscous liquid flowing inside a cylinder rotating about its horizontal axis. The inner surface of the cylinder is either uniformly hotter or colder than the enveloping air. The mass, momentum, and energy equations are simplified using thin-film approximation. The analytically obtained film thickness evolution equation consists of various dimensionless parameters such as gravitational number, Bond number, Biot number, thermoviscosity number, and Marangoni number. The viscosity of the liquid is considered as an exponential function of temperature. The viscosity increases (decreases) within the film thickness away from the inner surface of the cylinder when the surface is uniformly hotter (colder) than the atmosphere. For hotter (colder) surface, the film thickness on the rising side decreases (increases) when convective heat transfer at the free surface is increased. The surface tension gradient at the free surface generates Marangoni stress that has a destabilizing (stabilizing) effect on the thin film flow in the case of a hotter (colder) cylinder. The thermoviscosity number stabilizes (destabilizes) the flow on a heating (cooling) surface and this effect increases with an increase in the heat transfer at the free surface. For a hotter surface and in the presence of Marangoni stress, the convective heat transfer at the interface has the destabilizing effect for small values of the Biot number and assumes a stabilizing role for larger values. Non-linear simulations show consistency with the linear stability analysis.

  14. Stochastic modeling of mode interactions via linear parabolized stability equations

    Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

    2017-11-01

    Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

  15. A theorem for non-linear stability to tearing modes

    Avinash, K.

    1992-12-01

    Within the reduced MHD approximation it is shown that dJ z /dΨ≤0 [J z is z component of the current density and Ψ is the helical flux] is a sufficient condition for the equilibrium to be non-linearly stable to tearing mode. It is further shown that this is also a sufficient condition for an equilibrium to be axisymmetric, hence helical equilibrium consistent with this condition cannot be constructed. However a class of axisymmetric equilibrium with hollow current profile is shown to satisfy the stability criterion. (author). 16 refs, 2 figs

  16. Hydrodynamic theory of convective transport across a dynamically stabilized diffuse boundary layer

    Gerhauser, H.

    1983-09-01

    The diffuse boundary layer between miscible liquids is subject to Rayleigh-Taylor instabilities if the heavy fluid is supported by the light one. The resulting rapid interchange of the liquids can be suppressed by enforcing vertical oscillations on the whole system. This dynamic stabilization is incomplete and produces some peculiar novel transport phenomena such as decay off the density profile into several steps, periodic peeling of density sheets of the boundary layer and the appearance of steady vortex flow. The theory presented in this paper identifies the basic mechanism as formation of convective cells leading to enhanced diffusion, and explains previous experimental results with water and ZnJ 2 -solutions. A nonlinear treatment of the stationary convective flow problem gives the saturation amplitude of the ground mode and provides an upper bound for the maximum convective transport. The hydrodynamic model can be used for visualizing similar transport processes in the plasma of toroidal confinement devices such as sawtooth oscillations in soft disruptions of tokamak discharges and anomalous diffusion by excitation of convective cells. The latter process is investigated here in some detail, leading to the result that the maximum possible transport is of the order of Bohm diffusion. (orig.)

  17. Experimental Investigation on the Characteristics of Hydrodynamic Stabilities in Francis Hydroturbine Models

    Wen-Tao Su

    2014-03-01

    Full Text Available This paper presents an experimental investigation of flow phenomena related to the characteristic frequencies of pressure fluctuation in Francis hydroturbine models. The experiments were carried out on two test rigs with two model runners having hydraulic similarities. Flow field around the guide vanes was measured with a particle image velocimetry (PIV on the first PIV test rig. Flow structures at the inlet region of runner and in draft tube at different operating conditions were visualized on another hydrodynamic test rig. Analyses of dominant frequency of unsteady hydraulic behaviors in the tested hydroturbines were performed. It was observed that the main frequency of flow over the guide vanes and the dominant frequency of channel vortex equal the blade passing frequency; the dominant frequency of flow separation at the suction side of blade inlet equals the vane passing frequency; the vortex rope in the draft tube displays a low-frequency nature. The flow instabilities and fluctuations directly influence the running of hydroturbine, thus these experimental results could provide important evidence for the stability study of a real hydroturbine.

  18. Study of the hydrodynamic stability of natural-circulation steam generators

    Olive, J.

    1981-01-01

    This report presents a mathematical model of a study of the stability of natural-circulation steam generators. The method used consists in linearizing the equations for the single-dimensional flow and integrating them by using Laplace's transformation. The properties of the two-phase fluids are described by a homegeneous model with slip. The results of the calculation are the transfer functions of the circulation loop and its own oscillation modes (period and damping). Comparison of the results obtained by this method with those from other existing methods in the case of a straight tube with forced flow have proved satisfactory. Lastly, the results of a parametric study on the stability of a natural-circulation steam generator for a PWR unit are presented. The results show that the model is capable of reproducing at least qualitatively the trends observed experimentally or obtained by other more complex theoretical models [fr

  19. Hydrodynamic stability and Ti-tracer distribution in low-adiabat OMEGA direct-drive implosions

    Joshi, Tirtha R.

    We discuss the hydrodynamic stability of low-adiabat OMEGA direct-drive implosions based on results obtained from simultaneous emission and absorption spectroscopy of a titanium tracer added to the target. The targets were deuterium filled, warm plastic shells of varying thicknesses and filling gas pressures with a submicron Ti-doped tracer layer initially located on the inner surface of the shell. The spectral features from the titanium tracer are observed during the deceleration and stagnation phases of the implosion, and recorded with a time integrated spectrometer (XRS1), streaked crystal spectrometer (SSCA) and three gated, multi-monochromatic X-ray imager (MMI) instruments fielded along quasi-orthogonal lines-of-sight. The time-integrated, streaked and gated data show simultaneous emission and absorption spectral features associated with titanium K-shell line transitions but only the MMI data provides spatially resolved information. The arrays of gated spectrally resolved images recorded with MMI were processed to obtain spatially resolved spectra characteristic of annular contour regions on the image. A multi-zone spectroscopic analysis of the annular spatially resolved spectra permits the extraction of plasma conditions in the core as well as the spatial distribution of tracer atoms. In turn, the titanium atom distribution provides direct evidence of tracer penetration into the core and thus of the hydrodynamic stability of the shell. The observations, timing and analysis indicate that during fuel burning the titanium atoms have migrated deep into the core and thus shell material mixing is likely to impact the rate of nuclear fusion reactions, i.e. burning rate, and the neutron yield of the implosion. We have found that the Ti atom number density decreases towards the center in early deceleration phase, but later in time the trend is just opposite, i.e., it increases towards the center of the implosion core. This is in part a consequence of the convergent

  20. Reply to ``Comment on `Attractive forces between ions in quantum plasmas: Failure of linearized quantum hydrodynamics' ''

    Bonitz, M.; Pehlke, E.; Schoof, T.

    2013-03-01

    This is the last of a series of three papers. In the first [Phys. Rev. E10.1103/PhysRevE.87.033105 87, 033105 (2013)], the same authors presented a critical analysis of the prediction of “novel attractive forces” between protons in dense hydrogen put forward by Shukla and Eliasson in a recent Letter [Phys. Rev. Lett.10.1103/PhysRevLett.108.165007 108, 165007 (2012)]. Based on ab initio density functional theory (DFT) calculations and general considerations, it was shown that no such force exists. In the second of the three papers [Phys. Rev. E10.1103/PhysRevE.87.037101 87, 037101 (2013)], Shukla, Eliasson, and Akbari-Moghanjoughi (SEA) rejected this analysis. SEA did not discuss our arguments but claimed that the discrepancy between their quantum hydrodynamic model (QHD) and DFT is due to a failure of the latter. It is the purpose of the present Reply to demonstrate that this claim is incorrect because DFT is more accurate than QHD, by construction.

  1. A semi-analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using Buongiorno's mathematical model together with more realistic boundary conditions

    Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid

    2018-06-01

    The main aim of the present analysis is to examine the electroconvection phenomenon that takes place in a dielectric nanofluid under the influence of a perpendicularly applied alternating electric field. In this investigation, we assume that the nanofluid has a Newtonian rheological behavior and verifies the Buongiorno's mathematical model, in which the effects of thermophoretic and Brownian diffusions are incorporated explicitly in the governing equations. Moreover, the nanofluid layer is taken to be confined horizontally between two parallel plate electrodes, heated from below and cooled from above. In a fast pulse electric field, the onset of electroconvection is due principally to the buoyancy forces and the dielectrophoretic forces. Within the framework of the Oberbeck-Boussinesq approximation and the linear stability theory, the governing stability equations are solved semi-analytically by means of the power series method for isothermal, no-slip and non-penetrability conditions. In addition, the computational implementation with the impermeability condition implies that there exists no nanoparticles mass flux on the electrodes. On the other hand, the obtained analytical solutions are validated by comparing them to those available in the literature for the limiting case of dielectric fluids. In order to check the accuracy of our semi-analytical results obtained for the case of dielectric nanofluids, we perform further numerical and semi-analytical computations by means of the Runge-Kutta-Fehlberg method, the Chebyshev-Gauss-Lobatto spectral method, the Galerkin weighted residuals technique, the polynomial collocation method and the Wakif-Galerkin weighted residuals technique. In this analysis, the electro-thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical AC electric Rayleigh number Rec , whose value depends on several physical parameters. Furthermore, the effects of various pertinent parameters on the electro-thermo-hydrodynamic

  2. Stability and complexity of small random linear systems

    Hastings, Harold

    2010-03-01

    We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.

  3. Linear and nonlinear stability of periodic orbits in annular billiards

    Dettmann, Carl P.; Fain, Vitaly

    2017-04-01

    An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

  4. Linear model applied to the evaluation of pharmaceutical stability data

    Renato Cesar Souza

    2013-09-01

    Full Text Available The expiry date on the packaging of a product gives the consumer the confidence that the product will retain its identity, content, quality and purity throughout the period of validity of the drug. The definition of this term in the pharmaceutical industry is based on stability data obtained during the product registration. By the above, this work aims to apply the linear regression according to the guideline ICH Q1E, 2003, to evaluate some aspects of a product undergoing in a registration phase in Brazil. With this propose, the evaluation was realized with the development center of a multinational company in Brazil, with samples of three different batches composed by two active principal ingredients in two different packages. Based on the preliminary results obtained, it was possible to observe the difference of degradation tendency of the product in two different packages and the relationship between the variables studied, added knowledge so new models of linear equations can be applied and developed for other products.

  5. Linear Stability Analysis of an Acoustically Vaporized Droplet

    Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi

    2015-11-01

    Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.

  6. Hydrodynamic parameters of linear aromatic polyester of 3-phenylglutaric acid and bisphenol A

    Netopilík, Miloš; Kratochvíl, Jaroslav; Schallausky, F.; Reichelt, S.; Lederer, A.

    2007-01-01

    Roč. 12, č. 4 (2007), s. 285-300 ISSN 1023-666X R&D Projects: GA ČR GA203/07/0659; GA AV ČR IAA400500703 Institutional research plan: CEZ:AV0Z40500505 Keywords : chain parameters * linear polyester * size exclusion chromatography Subject RIV: CD - Macromolecular Chemistry Impact factor: 0.386, year: 2007

  7. The hydrodynamics of accretion discs. Pt. 1,2. Stability. Turbulent models

    Stewart, J

    1975-08-01

    The disc is idealized to be a stationary axisymmetric toroidal flow of a compressible fluid. The stability against linearized short wavelength perturbations is discussed. When the Rayleigh and Schwarzschild criteria are satisfied, the flow is stable against axisymmetric perturbations. However, almost all non-axisymmetric perturbations are not secularly stable, and examples of dynamically unstable modes are given. For turbulent models, two new points are made. The crucial problem for the horizontal structure of the disc, the prescription of the Reynolds stress gradient, is resolved by a direct calculation from first principles. A preliminary attempt is also made to describe the vertical structure, leading to a sandwich model. The predictions of this theory are shown to be consistent with the fine scale structure of Cyg X-1. (DE)

  8. Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

    Wienkers, A. F.; Ogilvie, G. I.

    2018-04-01

    Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalises the often-used cartesian shearing box model. The numerical method is an overall second order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localise the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of "bursty" dynamics such as the superhump phenomenon.

  9. The flow and hydrodynamic stability of a liquid film on a rotating disc

    Kim, Tae-Sung; Kim, Moon-Uhn

    2009-01-01

    The flow of a liquid film on a rotating disc is investigated in the case where a liquid is supplied at a constant flow rate. We propose thin film equations by the integral method with a simple approach to satisfy the boundary conditions on a disc and a free surface, and the results are compared with those of the Navier-Stokes equations. The radial film velocity is assumed to be a quartic profile in our analysis, whereas it was assumed to be a quadratic one, neglecting the inertia force so that the boundary conditions were not completely satisfied, in the analysis of Sisoev et al (2003 J. Fluid Mech. 229 531-54). The basic flow and its stability are analyzed using the thin film equations even in the region where the inertia force is not negligible. A local stability analysis of the flow is conducted using the linearized disturbance equations and correctly predicts Needham's simple instability criterion. The present thin film equations give a good approximation of the Navier-Stokes equations.

  10. Linear dimensional stability of elastomeric impression materials over time.

    Garrofé, Analía B; Ferrari, Beatriz A; Picca, Mariana; Kaplan, Andrea E

    2011-01-01

    The purpose of this study was to evaluate the linear dimensional stability of different elastomeric impression materials over time. A metal mold was designed with its custom trays, which were made of thermoplastic sheets (Sabilex sheets 0.125 mm thick). Three impressions were taken of it with each of the following: the polyvinylsiloxane Examix-GC-(AdEx), Aquasil-Dentsply-(AdAq) and Panasil-Kettenbach-(AdPa), and the polydimethylsiloxane Densell-Dental Medrano-(CoDe), Speedex-Coltene-(CoSp) and Lastic-Kettenbach-(CoLa). All impressions were taken with putty and light-body materials using a one-step technique. Standardized digital photographs were taken at different time intervals (0, 15, 30, 60, 120 minutes; 24 hours; 7 and 14 days), using an "ad-hoc" device, and analyzed using software (Image Tool) by measuring the distance between lines previously made at the top of the mold. The results were analyzed by ANOVA for repeated measures. The initial and final values for mean and SD were: AdEx: 1.32 (0.01) and 1.31 (0.00); AdAq: 1.32 (0.00) and 1.32 (0.00), AdPa: 1.327 (0.006) and 1.31 (0.00); CoDe: 1.32 (0.00) and 1.32 (0.01); CoSp: 1.327 (0.006) and 1.31 (0.00), CoLa: 1.327 (0.006) and 1.303 (0.006). Statistical evaluation showed that both material and time have significant effects. Under the conditions in this study we conclude that time would significantly affect the lineal dimensional stability of elastomeric impression materials.

  11. Application of linearized model to the stability analysis of the pressurized water reactor

    Li Haipeng; Huang Xiaojin; Zhang Liangju

    2008-01-01

    A Linear Time-Invariant model of the Pressurized Water Reactor is formulated through the linearization of the nonlinear model. The model simulation results show that the linearized model agrees well with the nonlinear model under small perturbation. Based upon the Lyapunov's First Method, the linearized model is applied to the stability analysis of the Pressurized Water Reactor. The calculation results show that the methodology of linearization to stability analysis is conveniently feasible. (authors)

  12. Frequency prediction by linear stability analysis around mean flow

    Bengana, Yacine; Tuckerman, Laurette

    2017-11-01

    The frequency of certain limit cycles resulting from a Hopf bifurcation, such as the von Karman vortex street, can be predicted by linear stability analysis around their mean flows. Barkley (2006) has shown this to yield an eigenvalue whose real part is zero and whose imaginary part matches the nonlinear frequency. This property was named RZIF by Turton et al. (2015); moreover they found that the traveling waves (TW) of thermosolutal convection have the RZIF property. They explained this as a consequence of the fact that the temporal Fourier spectrum is dominated by the mean flow and first harmonic. We could therefore consider that only the first mode is important in the saturation of the mean flow as presented in the Self-Consistent Model (SCM) of Mantic-Lugo et al. (2014). We have implemented a full Newton's method to solve the SCM for thermosolutal convection. We show that while the RZIF property is satisfied far from the threshold, the SCM model reproduces the exact frequency only very close to the threshold. Thus, the nonlinear interaction of only the first mode with itself is insufficiently accurate to estimate the mean flow. Our next step will be to take into account higher harmonics and to apply this analysis to the standing waves, for which RZIF does not hold.

  13. Survey of non-linear hydrodynamic models of type-II Cepheids

    Smolec, R.

    2016-03-01

    We present a grid of non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6 M⊙ and a range of metallicities ([Fe/H] = -2.0, -1.5, -1.0), and for 0.8 M⊙ ([Fe/H] = -1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models, violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russell diagram, we detect two domains in which period-doubled pulsation is possible. The first extends through the BL Her domain and low-luminosity W Vir domain (pulsation periods ˜2-6.5 d). The second domain extends at higher luminosities (W Vir domain; periods >9.5 d). Some models within these domains display period-4 pulsation. We also detect very narrow domains (˜10 K wide) in which modulation of pulsation is possible. Another interesting phenomenon we detect is double-mode pulsation in the fundamental mode and in the fourth radial overtone. Fourth overtone is a surface mode, trapped in the outer model layers. Single-mode pulsation in the fourth overtone is also possible on the hot side of the classical instability strip. The origin of the above phenomena is discussed. In particular, the role of resonances in driving different pulsation dynamics as well as in shaping the morphology of the radius variation curves is analysed.

  14. STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS.

    Li, B O; Sun, Hui; Zhou, Shenggao

    The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

  15. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

  16. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

    Tadeusz Kaczorek

    2013-06-01

    Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

  17. Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

    Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

  18. A Method to Simulate Linear Stability of Impulsively Accelerated Density Interfaces in Ideal-MHD and Gas Dynamics

    Samtaney, Ravi

    2009-01-01

    We present a numerical method to solve the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the Richtmyer-Meshkov instability. The method uses an Eulerian approach, and is based on an unwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations. The method is applicable to either gas dynamics or magnetohydrodynamics. Numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface, and a doubly shocked single density interface. Convergence tests show that the method is spatially second order accurate for smooth flows, and between first and second order accurate for flows with shocks

  19. Survey of linear MHD stability in tokamak configurations

    Wakatani, M.

    1977-01-01

    The results found by MHD stability studies for both low-beta and high-beta tokamaks are reviewed. The stability against kink-ballooning modes in equilibria surrounded by vacuum or a layer of force free currents is considered. Internal kink modes and the relation to interchange modes, which should be considered after external kink modes are suppressed, are surveyed

  20. Non-Linear Aeroelastic Stability of Wind Turbines

    Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie

    2013-01-01

    trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...

  1. Classifying spaces with virtually cyclic stabilizers for linear groups

    Degrijse, Dieter Dries; Köhl, Ralf; Petrosyan, Nansen

    2015-01-01

    We show that every discrete subgroup of GL(n, ℝ) admits a finite-dimensional classifying space with virtually cyclic stabilizers. Applying our methods to SL(3, ℤ), we obtain a four-dimensional classifying space with virtually cyclic stabilizers and a decomposition of the algebraic K-theory of its...

  2. On stabilization of linear systems with stochastic disturbances and input saturation

    Stoorvogel, A.A.; Weiland, S.; Saberi, A.

    2004-01-01

    It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication

  3. Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

    Huiying Sun

    2014-01-01

    Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

  4. Kinetic Effects on the Stability Properties of Field-reversed Configurations: I. Linear Stability

    Elena V. Belova; Ronald C. Davidson; Hantao Ji; Masaaki Yamada

    2003-01-28

    New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs. The n = 1 tilt instability mechanism and growth rate reduction mechanisms are investigated in detail including resonant particle effects, finite Larmor radius and Hall stabilization, and profile effects. It is shown that the Hall effect determines the mode rotation and the change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to finite Larmor radius effects. Resonant wave-particle interactions are studied as a function of (a) elongation, (b) the kinetic parameter S*, which is proportional to the ratio of the separatrix radius to the thermal ion Larmor radius, and (c) the separatrix shape. It is demonstrated that, contrary to the usually assumed stochasticity of the ion orbits in the FRC, a large fraction of the orbits are regular in long configurations when S* is small. A stochasticity condition is found, and a scaling with the S* parameter is presented. Resonant particle effects are shown to maintain the instability in the large gyroradius regime regardless of the separatrix shape.

  5. SPORTS - a simple non-linear thermalhydraulic stability code

    Chatoorgoon, V.

    1986-01-01

    A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)

  6. Vibration Stabilization of a Mechanical Model of a X-Band Linear Collider Final Focus Magnet

    Frisch, J; Decker, V; Hendrickson, L; Markiewicz, T W; Partridge, R; Seryi, Andrei

    2004-01-01

    The small beam sizes at the interaction point of a X-band linear collider require mechanical stabilization of the final focus magnets at the nanometer level. While passive systems provide adequate performance at many potential sites, active mechanical stabilization is useful if the natural or cultural ground vibration is higher than expected. A mechanical model of a room temperature linear collider final focus magnet has been constructed and actively stabilized with an accelerometer based system.

  7. Vibration Stabilization of a Mechanical Model of a X-Band Linear Collider Final Focus Magnet

    Frisch, Josef; Chang, Allison; Decker, Valentin; Doyle, Eric; Eriksson, Leif; Hendrickson, Linda; Himel, Thomas; Markiewicz, Thomas; Partridge, Richard; Seryi, Andrei; SLAC

    2006-01-01

    The small beam sizes at the interaction point of a X-band linear collider require mechanical stabilization of the final focus magnets at the nanometer level. While passive systems provide adequate performance at many potential sites, active mechanical stabilization is useful if the natural or cultural ground vibration is higher than expected. A mechanical model of a room temperature linear collider final focus magnet has been constructed and actively stabilized with an accelerometer based system

  8. Linear stability analysis of collective neutrino oscillations without spurious modes

    Morinaga, Taiki; Yamada, Shoichi

    2018-01-01

    Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

  9. Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno's mathematical model

    Wakif, Abderrahim; Boulahia, Zoubair; Mishra, S. R.; Mehdi Rashidi, Mohammad; Sehaqui, Rachid

    2018-05-01

    The onset of nanofluid convection in the presence of an externally applied magnetic field is investigated numerically based on the non-homogeneous Buongiorno's mathematical model. In this study, we use the latest experimental correlations and powerful analytical models for expressing the thermo-physical properties of some electrically conducting nanofluids, such as copper-water, sliver-water and gold-water nanofluids, in which the Brownian motion and thermophoresis effects on slip flow in nanofluids are taken into account in this model ( i.e., two-phase transport model). In this paper, we assume that the nanofluid has Newtonian behavior, confined horizontally between two infinite impermeable boundaries and heated from below, in such a way that the nanoparticles tend to concentrate near the upper wall. Considering the basic state of the nanofluidic system, the linear stability theory has been successfully applied to obtain the principal stability equations, which are solved numerically for an imposed volumetric fraction of nanoparticles and no-slip impermeable conditions at the isothermal walls bounding the nanofluid layer. The linear boundary-value problem obtained in this investigation is converted into a pure initial-value problem, so that we can solve it numerically by the fourth-fifth-order Runge-Kutta-Fehlberg method. The generalized Buongiorno's mathematical model proposed in this study allows performing a highly accurate computational analysis. In addition, the obtained results show that the stability of the studied nanofluidic system depends on several parameters, namely, the magnetic Chandrasekhar number Q , the reference value for the volumetric fraction of nanoparticles φ_0 and the size of nanoparticles d_p . In this analysis, the thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical thermal Rayleigh number R_{ac} , which characterizes the onset of convection cells, whose size is L_c=2π/a_c . Furthermore, the effects

  10. Investigations on hydrodynamic stability of two phase flow in a low pressure natural circulation system

    Shaorong, Wu; Dazhong, Wang; Meisheng, Yao; Jinhai, Bo; Yunxian, Tong; Shengyao, Jiang; Bing, Han [Institute of Nuclear Energy and Technology, Tsingua Univ., Beijing (China)

    1997-09-01

    Appropriately scaled ``Loop Stability`` tests and ``Channel Stability`` tests were performed with single heated channel system and two parallel channel system separately at the Institute of Nuclear Energy Technology (INET) of the Tsinghua University in China. A broad range of several operational parameters such as heating power, system pressure, test inlet subcooling and resistance coefficient were investigated. It was found that under certain geometric conditions and operating parameters a self-sustaining, low frequency, even amplitude mass flow oscillation may be excited at very low steam qualities and subcooling conditions. Stability maps under different conditions have been provided to assist the design of the NHR. (author). 6 refs, 15 figs.

  11. Hydrodynamic Fluid Film Bearings and Their Effect on the Stability of Rotating Machinery

    Andres, Luis S

    2006-01-01

    .... This design parameter shows the static performance of the bearing as rotor speed increases. Rotordynamic force coefficients are introduced and their effect on the stability of a rotor-bearing system thoroughly discussed...

  12. STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS

    Pagliari Carmen

    2013-07-01

    Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to

  13. Evaluation of Thin Plate Hydrodynamic Stability through a Combined Numerical Modeling and Experimental Effort

    Tentner, A. [Argonne National Lab. (ANL), Argonne, IL (United States); Bojanowski, C. [Argonne National Lab. (ANL), Argonne, IL (United States); Feldman, E. [Argonne National Lab. (ANL), Argonne, IL (United States); Wilson, E. [Argonne National Lab. (ANL), Argonne, IL (United States); Solbrekken, G [Univ. of Missouri, Columbia, MO (United States); Jesse, C. [Univ. of Missouri, Columbia, MO (United States); Kennedy, J. [Univ. of Missouri, Columbia, MO (United States); Rivers, J. [Univ. of Missouri, Columbia, MO (United States); Schnieders, G. [Univ. of Missouri, Columbia, MO (United States)

    2017-05-01

    An experimental and computational effort was undertaken in order to evaluate the capability of the fluid-structure interaction (FSI) simulation tools to describe the deflection of a Missouri University Research Reactor (MURR) fuel element plate redesigned for conversion to lowenriched uranium (LEU) fuel due to hydrodynamic forces. Experiments involving both flat plates and curved plates were conducted in a water flow test loop located at the University of Missouri (MU), at conditions and geometries that can be related to the MURR LEU fuel element. A wider channel gap on one side of the test plate, and a narrower on the other represent the differences that could be encountered in a MURR element due to allowed fabrication variability. The difference in the channel gaps leads to a pressure differential across the plate, leading to plate deflection. The induced plate deflection the pressure difference induces in the plate was measured at specified locations using a laser measurement technique. High fidelity 3-D simulations of the experiments were performed at MU using the computational fluid dynamics code STAR-CCM+ coupled with the structural mechanics code ABAQUS. Independent simulations of the experiments were performed at Argonne National Laboratory (ANL) using the STAR-CCM+ code and its built-in structural mechanics solver. The simulation results obtained at MU and ANL were compared with the corresponding measured plate deflections.

  14. A Two-Dimensional Numerical Study of Hydrodynamic, Heat and Mass Transfer and Stability in a Salt Gradient Solar Pond

    Ali Ben Moussa

    2012-10-01

    Full Text Available In this work, the problem of hydrodynamic, heat and mass transfer and stability in a salt gradient solar pond has been numerically studied by means of computational fluid dynamics in transient regime. The body of the simulated pond is an enclosure of height H and length L wherein an artificial salinity gradient is created in order to suppress convective motions induced by solar radiation absorption and to stabilize the solar pond during the period of operation. Here we show the distribution of velocity, temperature and salt concentration fields during energy collection and storage in a solar pond filled with water and constituted by three different salinity zones. The bottom of the pond is blackened and the free-surface is subjected to heat losses by convection, evaporation and radiation while the vertical walls are adiabatic and impermeable. The governing equations of continuity, momentum, thermal energy and mass transfer are discretized by finite–volume method in transient regime. Velocity vector fields show the presence of thin convective cells in the upper convective zone (UCZ and large convective cells in the lower convective zone (LCZ. This study shows the importance of buoyancy ratio in the decrease of temperature in the UCZ and in the preservation of high temperature in the LCZ. It shows also the importance of the thickness of Non-Convective Zone (NCZ in the reduction of the upwards heat losses.

  15. Ionization effects and linear stability in a coaxial plasma device

    Kurt, Erol; Kurt, Hilal; Bayhan, Ulku

    2009-03-01

    A 2-D computer simulation of a coaxial plasma device depending on the conservation equations of electrons, ions and excited atoms together with the Poisson equation for a plasma gun is carried out. Some characteristics of the plasma focus device (PF) such as critical wave numbers a c and voltages U c in the cases of various pressures Pare estimated in order to satisfy the necessary conditions of traveling particle densities ( i.e. plasma patterns) via a linear analysis. Oscillatory solutions are characterized by a nonzero imaginary part of the growth rate Im ( σ) for all cases. The model also predicts the minimal voltage ranges of the system for certain pressure intervals.

  16. Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

    Hadjimichael, Yiannis; Ketcheson, David I.; Loczi, Lajos; Né meth, Adriá n

    2016-01-01

    Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order

  17. Automated finder for the critical condition on the linear stability of fluid motions

    Fujimura, Kaoru

    1990-03-01

    An automated finder routine for the critical condition on the linear stability of fluid motions is proposed. The Newton-Raphson method was utilized for an iteration to solve nonlinear eigenvalue problems appeared in the analysis. The routine was applied to linear stability problem of a free convection between vertical parallel plates with different non-uniform temperatures as well as a plane Poiseuille flow. An efficiency of the finder routine is demonstrated for several parameter sets, numerically. (author)

  18. Exponential stability of switched linear systems with time-varying delay

    Satiracoo Pairote

    2007-11-01

    Full Text Available We use a Lyapunov-Krasovskii functional approach to establish the exponential stability of linear systems with time-varying delay. Our delay-dependent condition allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. A simple procedure for constructing switching rule is also presented.

  19. The JPL Hg(sup +) Extended Linear Ion Trap Frequency Standard: Status, Stability, and Accuracy Prospects

    Tjoelker, R. L.; Prestage, J. D.; Maleki, L.

    1996-01-01

    Microwave frequency standards based on room temperature (sup 199)Hg(sup +) ions in a Linear Ion Trap (LITS) presently achieve a Signal to Noise and line Q inferred short frequency stability. Long term stability has been measured for averaging intervals up to 5 months with apparent sensitivity to variations in ion number/temperature limiting the flicker floor.

  20. Asymptotic stability of linearly evolving non-stationary modes in a ...

    attention and it is believed to shed important light on the unresolved .... number assumption and is termed as the triple-deck theory. Having ... to analyse asymptotically the linear and weakly non-linear stability features of the station- ..... A numerical integration of equations (7–9) was implemented first to obtain the basic flow.

  1. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

    Hai Zhang

    2014-01-01

    Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

  2. Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems

    Morten Hovd

    2018-01-01

    Full Text Available The calculation of piecewise quadratic (PWQ Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI approach proposed in (Johansson and Rantzer, 1998 for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.

  3. Simulation and linear stability of traffic jams; Kotsu jutai no senkei anteisei to simulation

    Muramatsu, M. [Shizuoka University, Shizuoka (Japan); Nagatani, T. [Shizuoka University, Shizuoka (Japan). Faculty of Engineering

    1999-05-25

    A traffic jam induced by slowing down is investigated using simulation techniques of molecular dynamics. When cars are decelerated by the presence of hindrance, two typical traffic jams occur behind the hindrance: one is an oscillating jam and the other is a homogeneous jam. When the slowing down is small, the oscillating jam occurs. If the slowing down is large, the jam is homogeneous over space and time. Also, a backward propagating soliton-like jam is observed. The linear stability theory is applied to the traffic flow. The phase boundary between the oscillating and homogeneous jams is compared with the neutral stability line obtained by the linear stability theory. (author)

  4. Stability and linearity control of spectrometric channels of the Cherenkov counters using controllable units

    Kollar, D.; Kollarova, L.; Khorvat, P.

    1976-01-01

    A system is elaborated to control stability and linearity of the Cherenkov counter spectrometric channels in an experiment on a magnetic monopole search. Linearity of a light characteristic of a photoelectric multiplier is checked with the help of the calibrated light-strikings of light emitting diodes with flare intensity adjusted by controlling generator voltage across the mercury body. A program algorithm is presented for checking stability and linearity of the Cherenkov counter spectrometric channels which helps to consider the fatigue effects of the photoelectric multiplier resulting from the considerable loads

  5. Dose linearity and monitor unit stability of a G4 type cyberknife robotic stereotactic radiosurgery system

    Sudahar, H.; Kurup, P.G.G.; Murali, V.; Velmurugan, J.

    2012-01-01

    Dose linearity studies on conventional linear accelerators show a linearity error at low monitor units (MUs). The purpose of this study was to establish the dose linearity and MU stability characteristics of a cyberknife (Accuracy Inc., USA) stereotactic radiosurgery system. Measurements were done at a depth of 5 cm in a stereotactic dose verification phantom with a source to surface distance of 75 cm in a Generation 4 (G4) type cyberknife system. All the 12 fixed-type collimators starting from 5 to 60 mm were used for the dose linearity study. The dose linearity was examined in small (1-10), medium (15-100) and large (125-1000) MU ranges. The MU stability test was performed with 60 mm collimator for 10 MU and 20 MU with different combinations. The maximum dose linearity error of -38.8% was observed for 1 MU with 5 mm collimator. Dose linearity error in the small MU range was considerably higher than in the medium and large MU ranges. The maximum error in the medium range was -2.4%. In the large MU range, the linearity error varied between -0.7% and 1.2%. The maximum deviation in the MU stability was -3.03%. (author)

  6. Robust Stability and H∞ Control of Uncertain Piecewise Linear Switched Systems with Filippov Solutions

    Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal

    2012-01-01

    This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in fini...... algorithm is proposed to surmount the aforementioned matrix inequality conditions....... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...... inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H∞ per- formance are formulated. Finally, a V-K iteration...

  7. Linear stability analysis of a levitated nanomagnet in a static magnetic field: Quantum spin stabilized magnetic levitation

    Rusconi, C. C.; Pöchhacker, V.; Cirac, J. I.; Romero-Isart, O.

    2017-10-01

    We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that, apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.

  8. The hydrodynamic dust retention modeling process with a foam layer for open linear dynamic technological systems at construction industry enterprises

    Bespalov Vadim

    2017-01-01

    Full Text Available The physical essence of the reducing air pollution hydrodynamic method by means of the foamy method as the most effective dust retention technology for open long sources at construction industry enterprises is presented in the article. The mathematical description of this technology has been performed, taking into account the physical and chemical properties of the dust and foam bubble, as well as the parameters of the return of dust particles to technological raw material due to various physical mechanisms for their capture. The obtained parametric dependence of dust retention efficiency provides the possibility of its predicted calculation as a resultant parameter for the considering technology, taking into account the interaction of dust with a foam layer.

  9. Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

    Grigoriu, Mircea; Samorodnitsky, Gennady

    2004-01-01

    Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

  10. Determination Of The QUART Ion Chamber Stability By Using Medical Linear Accelerator

    Nasukha.

    1990-01-01

    The Quality Assurance Radiation Therapy (QUART) ion chamber was designed for quality assurance measurements of the medical linear accelerator at the Department of Radiation Oncology, Westmead Hospital in Sydney-Australia. The ion chamber has been calibrated by using the 6 MV medical linear accelerator against the farmer dosimeter. The Medical Physics Department Protocol, Westmead Hospital, Sydney (Australia) was used to check the stability of QUART ion chamber by determination of calibration factor for a period of time. It was found that the stability of the seven chambers were less than 2% for more than 125 days. (author). 4 refs, 7 figs

  11. Asymptotic Stabilization of Continuous-Time Linear Systems with Input and State Quantizations

    Sung Wook Yun

    2014-01-01

    Full Text Available This paper discusses the asymptotic stabilization problem of linear systems with input and state quantizations. In order to achieve asymptotic stabilization of such systems, we propose a state-feedback controller comprising two control parts: the main part is used to determine the fundamental characteristics of the system associated with the cost, and the additional part is employed to eliminate the effects of input and state quanizations. In particular, in order to implement the additional part, we introduce a quantizer with a region-decision making process (RDMP for a certain linear switching surface. The simulation results show the effectiveness of the proposed controller.

  12. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    Kabanov, Dmitry; Kasimov, Aslan R.

    2018-01-01

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  13. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    Kabanov, Dmitry I.

    2017-12-08

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  14. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    Kabanov, Dmitry

    2018-03-20

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  15. Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

    Songlin Wo

    2014-01-01

    Full Text Available The finite-time stability (FTS problem of discrete-time linear singular systems (DTLSS is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

  16. Quasi-stability of a vector trajectorial problem with non-linear partial criteria

    Vladimir A. Emelichev

    2003-10-01

    Full Text Available Multi-objective (vector combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05, 90C29, 90C31.

  17. Global stabilization of linear continuous time-varying systems with bounded controls

    Phat, V.N.

    2004-08-01

    This paper deals with the problem of global stabilization of a class of linear continuous time-varying systems with bounded controls. Based on the controllability of the nominal system, a sufficient condition for the global stabilizability is proposed without solving any Riccati differential equation. Moreover, we give sufficient conditions for the robust stabilizability of perturbation/uncertain linear time-varying systems with bounded controls. (author)

  18. General methods for determining the linear stability of coronal magnetic fields

    Craig, I. J. D.; Sneyd, A. D.; Mcclymont, A. N.

    1988-01-01

    A time integration of a linearized plasma equation of motion has been performed to calculate the ideal linear stability of arbitrary three-dimensional magnetic fields. The convergence rates of the explicit and implicit power methods employed are speeded up by using sequences of cyclic shifts. Growth rates are obtained for Gold-Hoyle force-free equilibria, and the corkscrew-kink instability is found to be very weak.

  19. The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

    Johnson, Thomas

    2018-01-01

    In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

  20. The Linear Stability Properties of Medium- to High- n TAEs in ITER

    Gorelenkov, N N; Budny, R V; Kessel, C E; Kramer, G J; McCune, D; Manickam, J; Nazikian, R

    2008-02-14

    This document provides a detailed report on the successful completion of the DOE OFES Theory Milestone for FY2007: Improve the simulation resolution of linear stability properties of Toroidal Alfvén Eigenmodes (TAE) driven by energetic particles and neutral beams in ITER by increasing the numbers of toroidal modes used to 15.

  1. The linear stability analysis of MHD models in axisymmetric toroidal geometry

    Manickam, J.; Grimm, R.C.; Dewar, R.L.

    1981-01-01

    A computational model to analyze the linear stability properties of general toroidal systems in the ideal magnetohydrodynamic limits is presented. This model includes an explicit treatment of the asymptotic singular behaviour at rational surfaces. It is verified through applications to internal kink modes. (orig.)

  2. Hyers-Ulam stability for second-order linear differential equations with boundary conditions

    Pasc Gavruta

    2011-06-01

    Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.

  3. The Effects of Radiation on the Linear Stability of a horizontal layer ...

    The effect of radiation on the onset of Rayleigh-Benard convection is studied in the case of a radiating Newtonian fluid in a fluid-saturated horizontal porous layer heated from below. The radiative heat transfer is treated using the differential approximation for optically thin limiting case. The linear stability theory is employed ...

  4. Lyapunov stability robust analysis and robustness design for linear continuous-time systems

    Luo, J.S.; Johnson, A.; Bosch, van den P.P.J.

    1995-01-01

    The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is

  5. Modeling the influence of storms on sand wave formation : A linear stability approach

    Campmans, G.H.P.; Roos, P.C.; de Vriend, H.J.; Hulscher, S.J.M.H.

    2017-01-01

    We present an idealized process-based morphodynamic model to study the effect of storms on sand wave formation. To this end, we include wind waves, wind-driven flow and, in addition to bed load transport, suspended load sediment transport. A linear stability analysis is applied to systematically

  6. Linear time delay methods and stability analyses of the human spine. Effects of neuromuscular reflex response.

    Franklin, Timothy C; Granata, Kevin P; Madigan, Michael L; Hendricks, Scott L

    2008-08-01

    Linear stability methods were applied to a biomechanical model of the human musculoskeletal spine to investigate effects of reflex gain and reflex delay on stability. Equations of motion represented a dynamic 18 degrees-of-freedom rigid-body model with time-delayed reflexes. Optimal muscle activation levels were identified by minimizing metabolic power with the constraints of equilibrium and stability with zero reflex time delay. Muscle activation levels and associated muscle forces were used to find the delay margin, i.e., the maximum reflex delay for which the system was stable. Results demonstrated that stiffness due to antagonistic co-contraction necessary for stability declined with increased proportional reflex gain. Reflex delay limited the maximum acceptable proportional reflex gain, i.e., long reflex delay required smaller maximum reflex gain to avoid instability. As differential reflex gain increased, there was a small increase in acceptable reflex delay. However, differential reflex gain with values near intrinsic damping caused the delay margin to approach zero. Forward-dynamic simulations of the fully nonlinear time-delayed system verified the linear results. The linear methods accurately found the delay margin below which the nonlinear system was asymptotically stable. These methods may aid future investigations in the role of reflexes in musculoskeletal stability.

  7. Stability of numerical method for semi-linear stochastic pantograph differential equations

    Yu Zhang

    2016-01-01

    Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

  8. Stability of Coulomb crystals in a linear Paul trap with storage-ring-like confinement

    Kjærgaard, Niels; Mølhave, Kristian; Drewsen, Michael

    2002-01-01

    We report experiments on the stability of ion Coulomb crystals in a linear Paul trap with storage-ring-like confinement. The transverse dynamics of charged particles in a trap of this type is analogous to that of a fast beam traveling through a channel with periodic, magnetic alternating gradient...... confinement. The experimentally observed stability conditions for stationary crystals comply remarkably well with current theory of crystalline plasmas and beams.......We report experiments on the stability of ion Coulomb crystals in a linear Paul trap with storage-ring-like confinement. The transverse dynamics of charged particles in a trap of this type is analogous to that of a fast beam traveling through a channel with periodic, magnetic alternating gradient...

  9. Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

    Zhang, Ling

    2017-01-01

    The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

  10. Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations

    Ling Zhang

    2017-10-01

    Full Text Available Abstract The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs. It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order 1 2 $\\frac{1}{2}$ to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

  11. Steady state and linear stability analysis of a supercritical water natural circulation loop

    Sharma, Manish; Pilkhwal, D.S.; Vijayan, P.K.; Saha, D.; Sinha, R.K.

    2010-01-01

    Supercritical water (SCW) has excellent heat transfer characteristics as a coolant for nuclear reactors. Besides it results in high thermal efficiency of the plant. However, the flow can experience instabilities in supercritical water reactors, as the density change is very large for the supercritical fluids. A computer code SUCLIN using supercritical water properties has been developed to carry out the steady state and linear stability analysis of a SCW natural circulation loop. The conservation equations of mass, momentum and energy have been linearized by imposing small perturbation in flow rate, enthalpy, pressure and specific volume. The equations have been solved analytically to generate the characteristic equation. The roots of the equation determine the stability of the system. The code has been qualitatively assessed with published results and has been extensively used for studying the effect of diameter, height, heater inlet temperature, pressure and local loss coefficients on steady state and stability behavior of a Supercritical Water Natural Circulation Loop (SCWNCL). The present paper describes the linear stability analysis model and the results obtained in detail.

  12. On the Linear Stability of the Fifth-Order WENO Discretization

    Motamed, Mohammad

    2010-10-03

    We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.

  13. Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect

    Zhao Min; Sun Di-Hua; Tian Chuan

    2012-01-01

    By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic (AELH) model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries (KdV) equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered. (interdisciplinary physics and related areas of science and technology)

  14. Submarine hydrodynamics

    Renilson, Martin

    2015-01-01

    This book adopts a practical approach and presents recent research together with applications in real submarine design and operation. Topics covered include hydrostatics, manoeuvring, resistance and propulsion of submarines. The author briefly reviews basic concepts in ship hydrodynamics and goes on to show how they are applied to submarines, including a look at the use of physical model experiments. The issues associated with manoeuvring in both the horizontal and vertical planes are explained, and readers will discover suggested criteria for stability, along with rudder and hydroplane effectiveness. The book includes a section on appendage design which includes information on sail design, different arrangements of bow planes and alternative stern configurations. Other themes explored in this book include hydro-acoustic performance, the components of resistance and the effect of hull shape. Readers will value the author’s applied experience as well as the empirical expressions that are presented for use a...

  15. Linear stability analysis of laminar flow near a stagnation point in the slip flow regime

    Essaghir, E.; Oubarra, A.; Lahjomri, J.

    2017-12-01

    The aim of the present contribution is to analyze the effect of slip parameter on the stability of a laminar incompressible flow near a stagnation point in the slip flow regime. The analysis is based on the traditional normal mode approach and assumes parallel flow approximation. The Orr-Sommerfeld equation that governs the infinitesimal disturbance of stream function imposed to the steady main flow, which is an exact solution of the Navier-Stokes equation satisfying slip boundary conditions, is obtained by using the powerful spectral Chebyshev collocation method. The results of the effect of slip parameter K on the hydrodynamic characteristics of the base flow, namely the velocity profile, the shear stress profile, the boundary layer, displacement and momentum thicknesses are illustrated and discussed. The numerical data for these characteristics, as well as those of the eigenvalues and the corresponding wave numbers recover the results of the special case of no-slip boundary conditions. They are found to be in good agreement with previous numerical calculations. The effects of slip parameter on the neutral curves of stability, for two-dimensional disturbances in the Reynolds-wave number plane, are then obtained for the first time in the slip flow regime for stagnation point flow. Furthermore, the evolution of the critical Reynolds number against the slip parameter is established. The results show that the critical Reynolds number for instability is significantly increased with the slip parameter and the flow turn out to be more stable when the effect of rarefaction becomes important.

  16. Classical linear-control analysis applied to business-cycle dynamics and stability

    Wingrove, R. C.

    1983-01-01

    Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

  17. COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

    Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp [Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)

    2016-03-15

    Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.

  18. Stability margin of linear systems with parameters described by fuzzy numbers.

    Husek, Petr

    2011-10-01

    This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.

  19. Application of Duflow for studying hydrodynamics and stability of tidal inlets in the Tam Giang - Cau Hai Lagoon

    Lam, N.T.; Verhagen, H.J.; Van der Wegen, M.

    2004-01-01

    This paper presents an application of an one-dimensional unsteady numerical model DUFLOW for hydrodynamic simulation of a complex lagoon-inlet system in Vietnam. The difficulties due to the lack of data for model boundary conditions is overcome by using sensitivity analysis approach for the

  20. Study of vibrations and stabilization of linear collider final doublets at the sub-nanometer scale

    Bolzon, B.

    2007-11-01

    CLIC is one of the current projects of high energy linear colliders. Vertical beam sizes of 0.7 nm at the time of the collision and fast ground motion of a few nanometers impose an active stabilization of the final doublets at a fifth of nanometer above 4 Hz. The majority of my work concerned vibrations and active stabilization study of cantilever and slim beams in order to be representative of the final doublets of CLIC. In a first part, measured performances of different types of vibration sensors associated to an appropriate instrumentation showed that accurate measurements of ground motion are possible from 0.1 Hz up to 2000 Hz on a quiet site. Also, electrochemical sensors answering a priori the specifications of CLIC can be incorporated in the active stabilization at a fifth of nanometer. In a second part, an experimental and numerical study of beam vibrations enabled to validate the efficiency of the numerical prediction incorporated then in the simulation of the active stabilization. Also, a study of the impact of ground motion and of acoustic noise on beam vibrations showed that an active stabilization is necessary at least up to 1000 Hz. In a third part, results on the active stabilization of a beam at its two first resonances are shown down to amplitudes of a tenth of nanometer above 4 Hz by using in parallel a commercial system performing passive and active stabilization of the clamping. The last part is related to a study of a support for the final doublets of a linear collider prototype in phase of finalization, the ATF2 prototype. This work showed that relative motion between this support and the ground is below imposed tolerances (6 nm above 0.1 Hz) with appropriate boundary conditions. (author)

  1. Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size

    Hadjimichael, Yiannis

    2016-09-08

    Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.

  2. An improved direct feedback linearization technique for transient stability enhancement and voltage regulation of power generators

    Kenne, Godpromesse [Laboratoire d' Automatique et d' Informatique Appliquee (LAIA), Departement de Genie Electrique, Universite de Dschang, B.P. 134 Bandjoun, Cameroun; Goma, Raphael; Lamnabhi-Lagarrigue, Francoise [Laboratoire des Signaux et Systemes (L2S), CNRS-SUPELEC, Universite Paris XI, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France); Nkwawo, Homere [Departement GEII, Universite Paris XIII, IUT Villetaneuse, 99 Avenue Jean Baptiste Clement, 93430 Villetaneuse (France); Arzande, Amir; Vannier, Jean Claude [Departement Energie, Ecole Superieure d' Electricite-SUPELEC, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France)

    2010-09-15

    In this paper, a simple improved direct feedback linearization design method for transient stability and voltage regulation of power systems is discussed. Starting with the classical direct feedback linearization technique currently applied to power systems, an adaptive nonlinear excitation control of synchronous generators is proposed, which is new and effective for engineering. The power angle and mechanical power input are not assumed to be available. The proposed method is based on a standard third-order model of a synchronous generator which requires only information about the physical available measurements of angular speed, active electric power and generator terminal voltage. Experimental results of a practical power system show that fast response, robustness, damping, steady-state and transient stability as well as voltage regulation are all achieved satisfactorily. (author)

  3. Numerical computation of the linear stability of the diffusion model for crystal growth simulation

    Yang, C.; Sorensen, D.C. [Rice Univ., Houston, TX (United States); Meiron, D.I.; Wedeman, B. [California Institute of Technology, Pasadena, CA (United States)

    1996-12-31

    We consider a computational scheme for determining the linear stability of a diffusion model arising from the simulation of crystal growth. The process of a needle crystal solidifying into some undercooled liquid can be described by the dual diffusion equations with appropriate initial and boundary conditions. Here U{sub t} and U{sub a} denote the temperature of the liquid and solid respectively, and {alpha} represents the thermal diffusivity. At the solid-liquid interface, the motion of the interface denoted by r and the temperature field are related by the conservation relation where n is the unit outward pointing normal to the interface. A basic stationary solution to this free boundary problem can be obtained by writing the equations of motion in a moving frame and transforming the problem to parabolic coordinates. This is known as the Ivantsov parabola solution. Linear stability theory applied to this stationary solution gives rise to an eigenvalue problem of the form.

  4. Stability, performance and sensitivity analysis of I.I.D. jump linear systems

    Chávez Fuentes, Jorge R.; González, Oscar R.; Gray, W. Steven

    2018-06-01

    This paper presents a symmetric Kronecker product analysis of independent and identically distributed jump linear systems to develop new, lower dimensional equations for the stability and performance analysis of this type of systems than what is currently available. In addition, new closed form expressions characterising multi-parameter relative sensitivity functions for performance metrics are introduced. The analysis technique is illustrated with a distributed fault-tolerant flight control example where the communication links are allowed to fail randomly.

  5. Stability Analysis of Periodic Orbits in a Class of Duffing-Like Piecewise Linear Vibrators

    El Aroudi, A.

    2014-09-01

    In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.

  6. Mathematical considerations regarding the stability of the trace element systems by linear regressions

    Mihai, Maria; Popescu, I.V.

    2002-01-01

    In this paper we present a mathematical model that would describe the stability and instability conditions, respectively of the organs of human body assumed as a living cybernetic system with feedback. We tested the theoretical model on the following trace elements: Mn, Zn and As. The trace elements were determined from the nose-pharyngeal carcinoma. We utilise the linear approximation to describe the dependencies between the trace elements determined in the hair of the patient. We present the results graphically. (authors)

  7. Dynamic stability of a vertically excited non-linear continuous system

    Náprstek, Jiří; Fischer, Cyril

    2015-01-01

    Roč. 155, July (2015), s. 106-114 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear systems * auto-parametric systems * semi-trivial solution * dynamic stability * system recovery * post- critical response Subject RIV: JM - Building Engineering Impact factor: 2.425, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045794915000024

  8. On the internal stability of non-linear dynamic inversion: application to flight control

    Alam, M.; Čelikovský, Sergej

    2017-01-01

    Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf

  9. Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

    Yongjin Li

    2013-08-01

    Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

  10. Stability Analysis of Periodic Orbits in a Class of Duffing-Like Piecewise Linear Vibrators

    El Aroudi, A.; Benadero, L.; Ouakad, H.; Younis, Mohammad I.

    2014-01-01

    In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.

  11. Maximizing mandibular prosthesis stability utilizing linear occlusion, occlusal plane selection, and centric recording.

    Williamson, Richard A; Williamson, Anne E; Bowley, John; Toothaker, Randy

    2004-03-01

    The stability of mandibular complete dentures may be improved by reducing the transverse forces on the denture base through linear (noninterceptive) occlusion, selecting an occlusal plane that reduces horizontal vectors of force at occlusal contact, and utilizing a central bearing intraoral gothic arch tracing to record jaw relations. This article is intended to acquaint the reader with one technique for providing stable complete denture prostheses using the aforementioned materials, devices, and procedures.

  12. Linear stability analysis of double ablation fronts in direct-drive inertial confinement fusion

    Yanez, C.; Sanz, J.; Ibanez, L. F.; Olazabal-Loume, M.

    2011-01-01

    A linear stability theory of double ablation fronts is developed for direct-drive inertial confinement fusion targets. The so-called electron radiative ablation front [S. Fujioka et al., Phys. Rev. Lett. 92, 195001 (2004)] is studied with a self-consistent model. Numerical results are presented as well as an analytical approach for the radiation dominated regime of very steep double ablation front structure. Dispersion relation formula is tackled by means of a sharp boundary model.

  13. On the linear stability of sheared and magnetized jets without current sheets - relativistic case

    Kim, Jinho; Balsara, Dinshaw S.; Lyutikov, Maxim; Komissarov, Serguei S.

    2018-03-01

    In our prior series of papers, we studied the non-relativistic and relativistic linear stability analysis of magnetized jets that do not have current sheets. In this paper, we extend our analysis to relativistic jets with a velocity shear and a similar current sheet free structure. The jets that we study are realistic because we include a velocity shear, a current sheet free magnetic structure, a relativistic velocity and a realistic thermal pressure so as to achieve overall pressure balance in the unperturbed jet. In order to parametrize the velocity shear, we apply a parabolic profile to the jets' 4-velocity. We find that the velocity shear significantly improves the stability of relativistic magnetized jets. This fact is completely consistent with our prior stability analysis of non-relativistic, sheared jets. The velocity shear mainly plays a role in stabilizing the short wavelength unstable modes for the pinch as well as the kink instability modes. In addition, it also stabilizes the long wavelength fundamental pinch instability mode. We also visualize the pressure fluctuations of each unstable mode to provide a better physical understanding of the enhanced stabilization by the velocity shear. Our overall conclusion is that combining velocity shear with a strong and realistic magnetic field makes relativistic jets even more stable.

  14. Linear stability of liquid films with phase change at the interface

    Spindler, Bertrand

    1980-01-01

    The objective of this research thesis is to study the linear stability of the flow of a liquid film on an inclined plane with a heat flow on the wall and an interfacial phase change, and to highlight the influence of the phase change on the flow stability. In order to do so, the author first proposed a rational simplification of equations by studying the order of magnitude of different terms, and based on some simple hypotheses regarding flow physics. Two stability studies are then addressed, one regarding a flow with a pre-existing film, and the other regarding the flow of a condensation film. In both cases, it is assumed that there is no imposed heat flow, but that the driving effect of vapour by the liquid film is taken into account [fr

  15. Linear stability of a fuel channel uniformly heated considering retrofeeding by vacuum. Theoretical study

    Gonzalez M, V.; Salinas H, J.G.; Espinosa P, G.

    2000-01-01

    The Technology, Regulation and Services Management of the National Commission of Nuclear Safety and Safeguards in coordinated form with the IPH Department of the Metropolitan Autonomous-Iztapalapa University, developed the present project to study the linear stability in a fuel channel uniformly heated with effects of retrofeeding by vacuums. In this study the methodology used in the analysis of linear stability of the nuclear reactor unit 1 at Laguna Verde power plant is described which represented by an average channel uniformly heated. The conceptual model consists of two cells which represent the two regions in which is divided the channel according to the cooling is in one and two phases, considering the boiling length dependent in the time. It is used the homogeneous flux models for describing the thermohydraulic behavior of the cooling in the two phases region. The neutron processes with the punctual model of the neutron kinetics with a group of retarded neutrons precursors are described. It is studied the behavior of the system in the frequency domain with the transfer functions obtained and it is characterized in four operation states corresponding to the four corners of the low stability zone in the map power-flow Laguna Verde power plant. For these operation states the characteristic frequency is determined and the corresponding Nyquist diagrams are obtained. The results show that the system stability depends on the power-flow relation and that the operations which implicate a reduction of this relation improve the stability of the system (reducing the power introducing control bars with constant cooling flow or increase cooling flow with bars pattern established). The obtained results with effects of retrofeeding by vacuums show that the value of the characteristic frequency is modified very little with respect to the model without retrofeeding, therefore the thermohydraulic processes seem to determine the response of the stability of the system

  16. Hydrodynamic description of the long-time tails of the linear and rotational velocity autocorrelation functions of a particle in a confined geometry.

    Frydel, Derek; Rice, Stuart A

    2007-12-01

    We report a hydrodynamic analysis of the long-time behavior of the linear and angular velocity autocorrelation functions of an isolated colloid particle constrained to have quasi-two-dimensional motion, and compare the predicted behavior with the results of lattice-Boltzmann simulations. Our analysis uses the singularity method to characterize unsteady linear motion of an incompressible fluid. For bounded fluids we construct an image system with a discrete set of fundamental solutions of the Stokes equation from which we extract the long-time decay of the velocity. For the case that there are free slip boundary conditions at walls separated by H particle diameters, the time evolution of the parallel linear velocity and the perpendicular rotational velocity following impulsive excitation both correspond to the time evolution of a two-dimensional (2D) fluid with effective density rho_(2D)=rhoH. For the case that there are no slip boundary conditions at the walls, the same types of motion correspond to 2D fluid motions with a coefficient of friction xi=pi(2)nu/H(2) modulo a prefactor of order 1, with nu the kinematic viscosity. The linear particle motion perpendicular to the walls also experiences an effective frictional force, but the time dependence is proportional to t(-2) , which cannot be related to either pure 3D or pure 2D fluid motion. Our incompressible fluid model predicts correct self-diffusion constants but it does not capture all of the effects of the fluid confinement on the particle motion. In particular, the linear motion of a particle perpendicular to the walls is influenced by coupling between the density flux and the velocity field, which leads to damped velocity oscillations whose frequency is proportional to c_(s)/H , with c_(s) the velocity of sound. For particle motion parallel to no slip walls there is a slowing down of a density flux that spreads diffusively, which generates a long-time decay proportional to t(-1) .

  17. Hydrodynamic of a deformed bubble in linear shear flow; Hydrodynamique d'une bulle deformee dans un ecoulement cisaille

    Adoua, S.R

    2007-07-15

    This work is devoted to the study of an oblate spheroidal bubble of prescribed shape set fixed in a linear shear flow using direct numerical simulation. The three dimensional Navier-Stokes equations are solved in orthogonal curvilinear coordinates using a finite volume method. The bubble response is studied over a wide range of the aspect ratio (1-2.7), the bubble Reynolds number (50-2000) and the non-dimensional shear rate (0.-1.2). The numerical simulations shows that the shear flow imposes a plane symmetry of the wake whatever the parameters of the flow. The trailing vorticity is organized into two anti-symmetrical counter rotating tubes with a sign imposed by the competition of two mechanisms (the Lighthill mechanism and the instability of the wake). Whatever the Reynolds number, the lift coefficient reaches the analytical value obtained in an inviscid, weakly sheared flow corresponding to a lift force oriented in the same direction as that of a spherical bubble. For moderate Reynolds numbers, the direction of the lift force reverses when the bubble aspect ratio is large enough as observed in experiments. This reversal occurs for aspect ratios larger than 2.225 and is found to be directly linked to the sign of the trailing vorticity which is concentrated within two counter-rotating threads which propel the bubble in a direction depending of their sign of rotation. The behavior of the drag does not revel any significant effect induced by the wake structure and follows a quadratic increase with the shear rate. Finally, the torque experienced by the bubble also reverses for the same conditions inducing the reversal of the lift force. By varying the orientation of the bubble in the shear flow, a stable equilibrium position is found corresponding to a weak angle between the small axis of the bubble and the flow direction. (author)

  18. Linear stability analysis of the gas injection augmented natural circulation of STAR-LM

    Yeon-Jong Yoo; Qiao Wu; James J Sienicki

    2005-01-01

    Full text of publication follows: A linear stability analysis has been performed for the gas injection augmented natural circulation of the Secure Transportable Autonomous Reactor - Liquid Metal (STAR-LM). Natural circulation is of great interest for the development of Generation-IV nuclear energy systems due to its vital role in the area of passive safety and reliability. One of such systems is STAR-LM under development by Argonne National Laboratory. STAR-LM is a 400 MWt class modular, proliferation-resistant, and passively safe liquid metal-cooled fast reactor system that uses inert lead (Pb) coolant and the advanced power conversion system that consists of a gas turbine Brayton cycle utilizing supercritical carbon dioxide (CO 2 ) to obtain higher plant efficiency. The primary loop of STAR-LM relies only on the natural circulation to eliminate the use of circulation pumps for passive safety consideration. To enhance the natural circulation of the primary coolant, STAR-LM optionally incorporates the additional driving force provided by the injection of noncondensable gas into the primary coolant above the reactor core, which is effective in removing heat from the core and transferring it to the secondary working fluid without the attainment of excessive coolant temperature at nominal operating power. Therefore, it naturally raises the concern about the natural circulation instability due to the relatively high temperature change in the core and the two-phase flow condition in the hot leg above the core. For the ease of analysis, the flow path of the loop was partitioned into five thermal-hydraulically distinct sections, i.e., heated core, unheated core, hot leg, heat exchanger, and cold leg. The one-dimensional single-phase flow field equations governing the natural circulation, i.e., continuity, momentum, and energy equations, were used for each section except the hot leg. For the hot leg, the one-dimensional homogeneous equilibrium two-phase flow field

  19. Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel

    Paul, Subhanker; Singh, Suneet

    2015-01-01

    The prime objective of the presented work is to develop a Nodalized Reduced Order Model (NROM) to carry linear stability analysis of flow instabilities in a two-phase flow system. The model is developed by dividing the single phase and two-phase region of a uniformly heated channel into N number of nodes followed by time dependent spatial linear approximations for single phase enthalpy and two-phase quality between the consecutive nodes. Moving boundary scheme has been adopted in the model, where all the node boundaries vary with time due to the variation of boiling boundary inside the heated channel. Using a state space approach, the instability thresholds are delineated by stability maps plotted in parameter planes of phase change number (N pch ) and subcooling number (N sub ). The prime feature of the present model is that, though the model equations are simpler due to presence of linear-linear approximations for single phase enthalpy and two-phase quality, yet the results are in good agreement with the existing models (Karve [33]; Dokhane [34]) where the model equations run for several pages and experimental data (Solberg [41]). Unlike the existing ROMs, different two-phase friction factor multiplier correlations have been incorporated in the model. The applicability of various two-phase friction factor multipliers and their effects on stability behaviour have been depicted by carrying a comparative study. It is also observed that the Friedel model for friction factor calculations produces the most accurate results with respect to the available experimental data. (authors)

  20. Stability Criterion of Linear Stochastic Systems Subject to Mixed H2/Passivity Performance

    Cheung-Chieh Ku

    2015-01-01

    Full Text Available The H2 control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the H2 control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.

  1. On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires

    Guelman, M [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires, services scientifiques

    1968-09-01

    A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [French] Dans ce travail, on etudie la stabilite absolue des systemes non lineaires utilisant la deuxieme methode de Liapounov en tenant compte des resultats acquis a partir des travaux de V.M. Popov. On fait d'abord un expose des resultats deja etablis, en particulier en ce qui concerne les criteres frequentiels de stabilite absolue pour le cas d'un systeme de commande automatique comportant une seule non linearite. On a prolonge ces resultats jusqu'a l'etablissement de l'existence d'une parabole limite. On fait ensuite une nouvelle utilisation des methodes etudiees, etablissant des criteres de stabilite absolue pour un systeme comportant un type different de non linearite. On etudie enfin les resultats obtenus, dans l'optique de la conjecture de Aizerman. (auteur)

  2. Impact of Crack on Stability of Slope with Linearly Increasing Undrained Strength

    Bing Li

    2018-01-01

    Full Text Available This paper presents a procedure for assessment of the impact of tension crack on stability of slope in clays with linearly increasing undrained strength. The procedure is based on the limit equilibrium method with variational extremization. The distribution of the normal stress over slip surface is mathematically obtained for slopes in clays with the linearly increasing undrained strength and then used to determine the tension crack for clays with zero tensile strength. The seismic effect is also included using the pseudostatic approach. Closed-form solutions to the minimum safety factor and the maximum crack depth can be derived and given in the form of chart for convenient use. The results demonstrate a significant effect of the tension crack on the stability of steep slopes, especially for strong seismic conditions. In this situation, neglecting the impact of tension crack in traditional ϕ=0 analyses may overestimate the slope safety. The most adverse location of the tension crack can be also determined and presented in the charts, which may be useful in designing reinforcements and remedial measures for slope stabilization.

  3. Real time computer control of a nonlinear Multivariable System via Linearization and Stability Analysis

    Raza, K.S.M.

    2004-01-01

    This paper demonstrates that if a complicated nonlinear, non-square, state-coupled multi variable system is smartly linearized and subjected to a thorough stability analysis then we can achieve our design objectives via a controller which will be quite simple (in term of resource usage and execution time) and very efficient (in terms of robustness). Further the aim is to implement this controller via computer in a real time environment. Therefore first a nonlinear mathematical model of the system is achieved. An intelligent work is done to decouple the multivariable system. Linearization and stability analysis techniques are employed for the development of a linearized and mathematically sound control law. Nonlinearities like the saturation in actuators are also been catered. The controller is then discretized using Runge-Kutta integration. Finally the discretized control law is programmed in a computer in a real time environment. The programme is done in RT -Linux using GNU C for the real time realization of the control scheme. The real time processes, like sampling and controlled actuation, and the non real time processes, like graphical user interface and display, are programmed as different tasks. The issue of inter process communication, between real time and non real time task is addressed quite carefully. The results of this research pursuit are presented graphically. (author)

  4. Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid model

    Sotnikov, V.I.; Paraschiv, I.; Makhin, V.; Bauer, B.S.; Leboeuf, J.N.; Dawson, J.M.

    2002-01-01

    A systematic study of the linear stage of sheared flow stabilization of Z-pinch plasmas based on the Hall fluid model with equilibrium that contains sheared flow and an axial magnetic field is presented. In the study we begin with the derivation of a general set of equations that permits the evaluation of the combined effect of sheared flow and axial magnetic field on the development of the azimuthal mode number m=0 sausage and m=1 kink magnetohydrodynamic (MHD) instabilities, with the Hall term included in the model. The incorporation of sheared flow, axial magnetic field, and the Hall term allows the Z-pinch system to be taken away from the region in parameter space where ideal MHD is applicable to a regime where nonideal effects tend to govern stability. The problem is then treated numerically by following the linear development in time of an initial perturbation. The numerical results for linear growth rates as a function of axial sheared flow, an axial magnetic field, and the Hall term are reported

  5. Analysis of the Covered Electrode Welding Process Stability on the Basis of Linear Regression Equation

    Słania J.

    2014-10-01

    Full Text Available The article presents the process of production of coated electrodes and their welding properties. The factors concerning the welding properties and the currently applied method of assessing are given. The methodology of the testing based on the measuring and recording of instantaneous values of welding current and welding arc voltage is discussed. Algorithm for creation of reference data base of the expert system is shown, aiding the assessment of covered electrodes welding properties. The stability of voltage–current characteristics was discussed. Statistical factors of instantaneous values of welding current and welding arc voltage waveforms used for determining of welding process stability are presented. The results of coated electrodes welding properties are compared. The article presents the results of linear regression as well as the impact of the independent variables on the welding process performance. Finally the conclusions drawn from the research are given.

  6. Linear kinetic stability of a field-reversed configuration with two ion components

    Staudenmeier, J.L.; Barnes, D.C.; Lewis, H.R.

    1990-01-01

    It has been suggested that a small fraction of non-axis encircling high energy ions may be sufficient to stabilize the tilt mode in a large s FRC. Experimental alteration of the ion distribution function in this manner might be achieved by rf heating the tail of the distribution function or by neutral beam injection. A linear Vlasov-fluid eigenfunction-eigenfrequency approach was used to investigate possible stabilization of the tilt mode by a high energy component. The ion distribution function is modeled as the sum of two Maxwellians with separate temperatures and no ion flow velocity. The cold component has a thermal s = 7, where s is the approximate number of ion gyroradii contained between the field null and the separatrix. The temperature ratio of the hot component to the cold component (T H /T T ) was varied from 2 to 100. Global hot particle fractions (n H ) up to ∼ .5 were used in the computations

  7. Removal Efficiency of Linear Alkyl Benzene Sulfonate (LAS in Yazd Stabilization Pond

    Asghar Ebrahimi

    2011-01-01

    Full Text Available Surfactants are organic chemicals with wide applications as detergents. Linear alkyl benzene sulfonate (LAS is an anionic surfactant most commonly used. Discharge of raw or treated wastewater containing this chemical into the environment causes major public health problems. In this study, 64 samples were taken from the effluent of Yazd Wastewater  Treatment Plant over a period of one year. The samples were analyzed according to standard methods. The results obtained from the samples taken in different seasons showed that the highest efficiency of anionic surfactant removal was achieved in the summer in the secondary facultative stabilization pond. The least efficiency was observed in the autumn in samples from the anaerobic stabilization pond. It was also found that treated wastewater discharged into surface waters, reused for agricultural irrigation, or discharged into absorbent wells had significant differences with Pvalue

  8. Linear systems with unstructured multiplicative uncertainty: Modeling and robust stability analysis.

    Radek Matušů

    Full Text Available This article deals with continuous-time Linear Time-Invariant (LTI Single-Input Single-Output (SISO systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed.

  9. Uniform stability for time-varying infinite-dimensional discrete linear systems

    Kubrusly, C.S.

    1988-09-01

    Stability for time-varying discrete linear systems in a Banach space is investigated. On the one hand, it established a fairly complete collection of necessary and sufficient conditions for uniform asymptotic equistability for input-free systems. This includes uniform and strong power equistability, and uniform and strong l p -equistability, among other technical conditions which also play essential role in stability theory. On other hand, it is shown that uniform asymptotic equistability for input-free systems is equivalent to each of the following concepts of uniform stability for forced systems: l p -input l p -state, c o -input c o -state, bounded-input bounded-state, l p>1 -input bounded-state, c sub (o)-input bounded-state, and convergent-input bounded-state; which are also equivalent to their nonuniform counterparts. For time-varying convergent systems, the above is also equivalent to convergent-input convergent-state stability. The proofs presented here are all ''elementary'' in the sense that they are based essentially only on the Banach-Steinhaus theorem. (autor) [pt

  10. Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

    Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

    1992-01-01

    Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

  11. Stability Analysis of Periodic Orbits in a Class of Duffing-Like Piecewise Linear Vibrators

    El Aroudi A.

    2014-01-01

    Full Text Available In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.

  12. Estimates of emittance dilution and stability in high-energy linear accelerators

    T. O. Raubenheimer

    2000-12-01

    Full Text Available In this paper, we present a series of analytic expressions to predict the beam dynamics in a long linear accelerator. These expressions can be used to model the linac optics, calculate the magnitude of the wakefields, estimate the emittance dilution due to misaligned accelerator components, and estimate the stability and jitter limitations. The analytic expressions are based on the results of simple physics models and are useful to understand the parameter sensitivities. They are also useful when using simple codes or spreadsheets to optimize a linac system.

  13. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  14. Global Uniform Asymptotic Stability of a Class of Switched Linear Systems with an Infinite Number of Subsystems

    L. F. Araghi

    2014-01-01

    Full Text Available Stability of switching systems with an infinite number of subsystems is important in some structure of systems, like fuzzy systems, neural networks, and so forth. Because of the relationship between stability of a set of matrices and switching systems, this paper first studies the stability of a set of matrices, then and the results are applied for stability of switching systems. Some new conditions for globally uniformly asymptotically stability (GUAS of discrete-time switched linear systems with an infinite number of subsystems are proposed. The paper considers some examples and simulation results.

  15. Stability and dynamical features of solitary wave solutions for a hydrodynamic-type system taking into account nonlocal effects

    Vladimirov, Vsevolod A.; Maçzka, Czesław; Sergyeyev, Artur; Skurativskyi, Sergiy

    2014-06-01

    We consider a hydrodynamic-type system of balance equations for mass and momentum closed by the dynamical equation of state taking into account the effects of spatial nonlocality. We study higher symmetry admitted by this system and establish its non-integrability for the generic values of parameters. A system of ODEs obtained from the system under study through the group theory reduction is investigated. The reduced system is shown to possess a family of the homoclinic solutions describing solitary waves of compression and rarefaction. The waves of compression are shown to be unstable. On the contrary, the waves of rarefaction are likely to be stable. Numerical simulations reveal some peculiarities of solitary waves of rarefaction, and, in particular, the recovery of their shape after the collisions.

  16. Stability of multi-objective bi-level linear programming problems under fuzziness

    Abo-Sinna Mahmoud A.

    2013-01-01

    Full Text Available This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC. First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

  17. Black hole nonmodal linear stability under odd perturbations: The Reissner-Nordström case

    Fernández Tío, Julián M.; Dotti, Gustavo

    2017-06-01

    Following a program on black hole nonmodal linear stability initiated by one of the authors [Phys. Rev. Lett. 112, 191101 (2014), 10.1103/PhysRevLett.112.191101], we study odd linear perturbations of the Einstein-Maxwell equations around a Reissner-Nordström anti-de Sitter black hole. We show that all the gauge invariant information in the metric and Maxwell field perturbations is encoded in the spacetime scalars F =δ (Fαβ *Fα β) and Q =δ (1/48 Cαβ γ δ *Cα β γ δ), where Cα β γ δ is the Weyl tensor, Fα β is the Maxwell field, a star denotes Hodge dual, and δ means first order variation, and that the linearized Einstein-Maxwell equations are equivalent to a coupled system of wave equations for F and Q . For a non-negative cosmological constant we prove that F and Q are pointwise bounded on the outer static region. The fields are shown to diverge as the Cauchy horizon is approached from the inner dynamical region, providing evidence supporting strong cosmic censorship. In the asymptotically anti-de Sitter case the dynamics depends on the boundary condition at the conformal timelike boundary, and there are instabilities if Robin boundary conditions are chosen.

  18. Modeling of Soil Aggregate Stability using Support Vector Machines and Multiple Linear Regression

    Ali Asghar Besalatpour

    2016-02-01

    Full Text Available Introduction: Soil aggregate stability is a key factor in soil resistivity to mechanical stresses, including the impacts of rainfall and surface runoff, and thus to water erosion (Canasveras et al., 2010. Various indicators have been proposed to characterize and quantify soil aggregate stability, for example percentage of water-stable aggregates (WSA, mean weight diameter (MWD, geometric mean diameter (GMD of aggregates, and water-dispersible clay (WDC content (Calero et al., 2008. Unfortunately, the experimental methods available to determine these indicators are laborious, time-consuming and difficult to standardize (Canasveras et al., 2010. Therefore, it would be advantageous if aggregate stability could be predicted indirectly from more easily available data (Besalatpour et al., 2014. The main objective of this study is to investigate the potential use of support vector machines (SVMs method for estimating soil aggregate stability (as quantified by GMD as compared to multiple linear regression approach. Materials and Methods: The study area was part of the Bazoft watershed (31° 37′ to 32° 39′ N and 49° 34′ to 50° 32′ E, which is located in the Northern part of the Karun river basin in central Iran. A total of 160 soil samples were collected from the top 5 cm of soil surface. Some easily available characteristics including topographic, vegetation, and soil properties were used as inputs. Soil organic matter (SOM content was determined by the Walkley-Black method (Nelson & Sommers, 1986. Particle size distribution in the soil samples (clay, silt, sand, fine sand, and very fine sand were measured using the procedure described by Gee & Bauder (1986 and calcium carbonate equivalent (CCE content was determined by the back-titration method (Nelson, 1982. The modified Kemper & Rosenau (1986 method was used to determine wet-aggregate stability (GMD. The topographic attributes of elevation, slope, and aspect were characterized using a 20-m

  19. First Integrals of Evolution Systems and Nonlinear Stability of Stationary Solutions for the Ideal Atmospheric, Oceanic Hydrodynamical and Plasma Models

    Gordin, V.A.

    1998-01-01

    First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)

  20. Equilibrium, stability and heating of plasmas in linear and toroidal Extrap pinches

    Bonnevier, B.; Drake, J.R.; Dalhed, H.E.

    1983-01-01

    The Extrap scheme consists of a Z-pinch immersed in an octupole field. The total magnetic field has no component along the pinch axis. Globally stable Z-pinch equilibria with a distributed plasma current density and a duration of about 100 Alfven transit times have been observed in linear and toroidal sector experiments. Theoretical studies indicate that this stability can be the result of constraints introduced by the octupole field and the resulting separatrix of the total field, in combination with finite-Larmor-radius effects. A scheme for ICRF heating of the plasma in configurations with a magnetic neutral line, being applicable to Extrap and FRC, is analysed. Wave propagation arises owing to the Hall effect. Particle resonances are responsible for the absorption, owing to a high parallel wavenumber and a weak magnetic field. (author)

  1. Chromatin Hydrodynamics

    Bruinsma, Robijn; Grosberg, Alexander Y.; Rabin, Yitzhak; Zidovska, Alexandra

    2014-01-01

    Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity. PMID:24806919

  2. Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

    Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

    2018-06-01

    Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

  3. Linearized stability analysis of thin-shell wormholes with a cosmological constant

    Lobo, Francisco S N; Crawford, Paulo

    2004-01-01

    Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows us to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analysed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for a 0 ≤ 3M the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius

  4. Linear Stability Analysis of Flow in an Internally Heated Rectangular Duct

    Uhlmann, M.

    2004-07-01

    The linear stability of flow in a vertical rectangular duct subject to homogeneous internal heating, constant-temperature no-slip walls and a driving pressure gradient is investigated numerically. A full Chebyshevbased Galerkin method is found to be more reliable than a collocation method, both including the elimination of the pressure and the stream wise velocity from the system of equations and making use of the full symmetry properties. A classification of the mean flow-obtained as a function of Grashof and Reynolds numbers and the geometrical aspect ratio in terms of its inflectional properties is proposed. It is found that the flow loses stability at all aspects rations for a combination of finite thermal buoyancy and pressure forces with opposed sings. In the square duct, the unstable region coincides with the range where additional inflection lines are observed the mean velocity profile. Unstable eigenfunctions are obtained for all basic symmetry modes and their structure can be described as slightly elongated pockets of cross-stream-vertical motion, training each other along the stream wise direction. (Author) 22 refs.

  5. Linear and nonlinear stability of a thermally stratified magnetically driven rotating flow in a cylinder.

    Grants, Ilmars; Gerbeth, Gunter

    2010-07-01

    The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by a rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilize the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. These rolls can only be excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this nonlinear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and nonlinear components of this transition by direct numerical simulation of the flow response to noise. It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.

  6. Microscopic model for the non-linear fluctuating hydrodynamic of {sup 4} He superfluid helium deduced by maximum entropy method; Modelo microscopico para la hidrodinamica fluctuante no lineal del {sup 4}He superfluido deducido mediante el metodo de maxima entropia

    Alvarez R, J.T

    1998-10-01

    This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ({sup 4} He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator {rho}hut{sub FP} that is evaluated as Wigneris function through {rho}{sub CG} obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D{sub mn} defined with a nonequilibrium coarse grained statistical operator {rho}hut{sub CG}, matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine {rho}hut{sub CG} by means of the local equilibrium statistical operator {rho}hut{sub l}-tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D{sub mn} but with aid of a quasi equilibrium statistical operator {rho}hut{sub qe} instead

  7. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  8. A non-linear reduced order methodology applicable to boiling water reactor stability analysis

    Prill, Dennis Paul

    2013-01-01

    Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

  9. Pattern formation in flocking models: A hydrodynamic description.

    Solon, Alexandre P; Caussin, Jean-Baptiste; Bartolo, Denis; Chaté, Hugues; Tailleur, Julien

    2015-12-01

    We study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models.

  10. Different ELM regimes at ASDEX upgrade and their linear stability analysis

    Burckhart, Andreas O.

    2013-01-01

    Edge localised modes (ELMs) are magnetohydrodynamic (MHD) instabilities that occur at the edge of magnetically confined fusion plasmas. They periodically expel particles and energy from the confined region. In addition to limiting the confinement, they cause high heat fluxes to the walls of the tokamak which may not be manageable in larger, next-generation devices. However, the exact nature of the instabilities that drive ELMs is still unknown. The most commonly invoked theory to explain the occurrence of ELMs is the peeling-ballooning model which posits a critical edge pressure gradient and current density. In this thesis, this model is tested against experimental data gathered at the ASDEX Upgrade (AUG) tokamak. For the first time, a broad selection of ELM scenarios is analysed with respect to ideal MHD stability using the same methodology. The comparison of experiment and theory is performed using a stability analysis chain, which consists of combining kinetic and magnetic measurements to generate self-consistent plasma equilibria with the Grad-Shafranov solver CLISTE, refining this equilibrium with the HELENA code, and, finally, determining its stability using ILSA, a linear MHD stability code. In theory the peeling ballooning model should apply to all type-I ELM scenarios. Therefore, the stability of several different type-I ELMy H-mode plasmas is analysed with respect to peeling ballooning modes. While some of them are consistent with the model, in others ELMs occur well below or above the ideal MHD stability limit. The standard type-I ELMy H-mode regime exhibits considerable variations with equilibria both well below and at the stability limit depending on the discharge. In addition, a nitrogen-seeded case in which the edge pressure gradient greatly exceeds the stability limit is identified. In another discharge, the edge pressure gradient and current density, which are on the threshold for marginal stability, relax when edge heating is applied. Contrary to

  11. Different ELM regimes at ASDEX upgrade and their linear stability analysis

    Burckhart, Andreas O.

    2013-12-16

    Edge localised modes (ELMs) are magnetohydrodynamic (MHD) instabilities that occur at the edge of magnetically confined fusion plasmas. They periodically expel particles and energy from the confined region. In addition to limiting the confinement, they cause high heat fluxes to the walls of the tokamak which may not be manageable in larger, next-generation devices. However, the exact nature of the instabilities that drive ELMs is still unknown. The most commonly invoked theory to explain the occurrence of ELMs is the peeling-ballooning model which posits a critical edge pressure gradient and current density. In this thesis, this model is tested against experimental data gathered at the ASDEX Upgrade (AUG) tokamak. For the first time, a broad selection of ELM scenarios is analysed with respect to ideal MHD stability using the same methodology. The comparison of experiment and theory is performed using a stability analysis chain, which consists of combining kinetic and magnetic measurements to generate self-consistent plasma equilibria with the Grad-Shafranov solver CLISTE, refining this equilibrium with the HELENA code, and, finally, determining its stability using ILSA, a linear MHD stability code. In theory the peeling ballooning model should apply to all type-I ELM scenarios. Therefore, the stability of several different type-I ELMy H-mode plasmas is analysed with respect to peeling ballooning modes. While some of them are consistent with the model, in others ELMs occur well below or above the ideal MHD stability limit. The standard type-I ELMy H-mode regime exhibits considerable variations with equilibria both well below and at the stability limit depending on the discharge. In addition, a nitrogen-seeded case in which the edge pressure gradient greatly exceeds the stability limit is identified. In another discharge, the edge pressure gradient and current density, which are on the threshold for marginal stability, relax when edge heating is applied. Contrary to

  12. The coupling of bay hydrodynamics with sediment supply and micro-tidal wetland stability under high rates of relative sea level rise

    Wang, J.; Xu, K.; Restreppo, G. A.; Bentley, S. J.; Meng, X.; Zhang, X.

    2017-12-01

    Due to global sea level rise, local subsidence and sediment deficit, the Mississippi River (MR) deltaic plain has lost a total of 25% of coastal Louisiana's wetlands during the last century, leading to huge losses of ecological services, economic and social crises. Ecosystem-based restoration strategies which rely on coastal system processes and feedbacks are urgently needed. Understanding linkages between estuarine and coastal systems and the adjacent marshlands will help the designing strategies. To investigate bay hydrodynamics and its impacts on the adjacent micro-tidal wetland stability, hourly measurements of wave, tidal current, and benthic sediment concentration in summer, winter, and spring of 2015-2016 were conducted in Fourleague Bay, Louisiana, USA. The bay-marsh system has been stable for almost 80 years under high relative sea level rising rate, which is 11 km southeast of the Atchafalaya River mouth, with a water depth of 1-3 m. High-temporal resolution data indicate that benthic sediment resuspension is mainly caused by wind-driven waves with a dominant periodicity of 4.8 d. The sediment flux reaches 28 g·m-1·s-1 per unit depth in cm during the events. Net sediment transport is northwestward in summer, and southeastward in winter and spring. Sediment flux available for surrounding marsh varies from 0-500 g·m-1·s-1. An optimal inundation depth of 50 cm is estimated by the equilibrium wetland elevation change model under high relative sea level rising rate of 1.57 cm·yr-1. Seasonal variations of river discharge and wind direction (particularly speeds >3 m·s-1) greatly impact potential sediment contribution from bay to the surrounding wetlands. Three sediment transport regimes are concluded based on the seasonal variations of river discharge and wind direction: the `bypassing' season, the resuspension-accumulation season, and the combined `bypassing' and resuspension-accumulation season. The bay hydrodynamic processes and their impacts on the

  13. Relativistic hydrodynamics

    Luciano, Rezzolla

    2013-01-01

    Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...

  14. EFFECTIVENESS OF WASTE STABILIZATION PONDS IN REMOVAL OF LINEAR ALKYL BENZENE SALFONATE (LAS

    Ahmed. M. Abdel-Rahman

    2013-06-01

    Full Text Available Detergents contain synthetic or organic surface active agents called surfactants, which are derived from petroleum product precursors. They have the common property of lowering the surface tensions of water thus allowing dirt or grease adhered to various articles to be washed off. Linear alkyl benzene sulfonate (LAS is a most commonly used anionic surfactant. Discharge of raw or treated wastewater containing this chemical substance into the environment causes major public health and enviromental problems. In this study, samples were taken from raw wastewater and effluents of treatment ponds of Elzaraby waste stabilization ponds over a period of one year. The treated effluent is either discharged into surface waters or re-used in agricultural irrigation. The samples were analyzed according to the standard methods. The results obtained from the samples taken in different seasons showed that the highest overall removal efficiency of LAS was achieved in summer season (77%, and the least efficiency was observed in Winter season (55%, while the maximum overall efficiency of BOD5 was in summer (88% and minimum efficiency was (73% in winter season. The Dissolved oxygen concentrations along the pond series (DO ranged from 0.18 to 4.8 mg/l.

  15. Linear stability and nonlinear dynamics of the fishbone mode in spherical tokamaks

    Wang, Feng; Liu, J. Y. [School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024 (China); Fu, G. Y.; Breslau, J. A. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States)

    2013-10-15

    Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the q{sub min} slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher q{sub min} values, consistent with the observed appearance of the fishbone before the “long-lived mode” in MAST and NSTX experiments. In contrast, at lower q{sub min} values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX.

  16. Inviscid linear stability analysis of two fluid columns of different densities subject to gravity

    Prathama, Aditya; Pantano, Carlos

    2017-11-01

    We investigate the inviscid linear stability of vertical interface between two fluid columns of different densities under the influence of gravity. In this flow arrangement, the two free streams are continuously accelerating, in contrast to the canonical Kelvin-Helmholtz or Rayleigh-Taylor instabilities whose base flows are stationary (or weakly time dependent). In these classical cases, the temporal evolution of the interface can be expressed as Fourier or Laplace solutions in time. This is not possible in our case; instead, we employ the initial value problem method to solve the equations analytically. The results, expressed in terms of the well-known parabolic cylinder function, indicate that the instability grows as the exponential of a quadratic function of time. The analysis shows that in this accelerating Kelvin-Helmholtz configuration, the interface is unconditionally unstable at all wave modes, despite the presence of surface tension. Department of Energy, National Nuclear Security Administration (Award No. DE-NA0002382) and the California Institute of Technology.

  17. Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

    Kuchment, Peter

    2015-05-10

    © 2015, Springer Basel. In the previous paper (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012), the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities could turn extremely unstable techniques, such as optical tomography or electrical impedance tomography, into stable, good-resolution procedures. It was shown that in all cases of interest, the Fréchet derivative of the forward mapping is a pseudo-differential operator with an explicitly computable principal symbol. If one can set up the imaging procedure in such a way that the symbol is elliptic, this would indicate that the problem was stabilized. In the cases when the symbol is not elliptic, the technique suggests how to change the procedure (e.g., by adding extra measurements) to achieve ellipticity. In this article, we consider the situation arising in acousto-optical tomography (also called ultrasound modulated optical tomography), where the internal data available involves the Green’s function, and thus depends globally on the unknown parameter(s) of the equation and its solution. It is shown that the technique of (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012) can be successfully adopted to this situation as well. A significant part of the article is devoted to results on generic uniqueness for the linearized problem in a variety of situations, including those arising in acousto-electric and quantitative photoacoustic tomography.

  18. Stability and performance analysis of a jump linear control system subject to digital upsets

    Wang, Rui; Sun, Hui; Ma, Zhen-Yang

    2015-04-01

    This paper focuses on the methodology analysis for the stability and the corresponding tracking performance of a closed-loop digital jump linear control system with a stochastic switching signal. The method is applied to a flight control system. A distributed recoverable platform is implemented on the flight control system and subject to independent digital upsets. The upset processes are used to stimulate electromagnetic environments. Specifically, the paper presents the scenarios that the upset process is directly injected into the distributed flight control system, which is modeled by independent Markov upset processes and independent and identically distributed (IID) processes. A theoretical performance analysis and simulation modelling are both presented in detail for a more complete independent digital upset injection. The specific examples are proposed to verify the methodology of tracking performance analysis. The general analyses for different configurations are also proposed. Comparisons among different configurations are conducted to demonstrate the availability and the characteristics of the design. Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61403395), the Natural Science Foundation of Tianjin, China (Grant No. 13JCYBJC39000), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China, the Tianjin Key Laboratory of Civil Aircraft Airworthiness and Maintenance in Civil Aviation of China (Grant No. 104003020106), and the Fund for Scholars of Civil Aviation University of China (Grant No. 2012QD21x).

  19. Kovasznay modes in the linear stability analysis of self-similar ablation flows

    Lombard, V.

    2008-12-01

    Exact self-similar solutions of gas dynamics equations with nonlinear heat conduction for semi-infinite slabs of perfect gases are used for studying the stability of ablative flows in inertial confinement fusion, when a shock wave propagates in front of a thermal front. Both the similarity solutions and their linear perturbations are numerically computed with a dynamical multi-domain Chebyshev pseudo-spectral method. Laser-imprint results, showing that maximum amplification occurs for a laser-intensity modulation of zero transverse wavenumber have thus been obtained (Abeguile et al. (2006); Clarisse et al. (2008)). Here we pursue this approach by proceeding for the first time to an analysis of perturbations in terms of Kovasznay modes. Based on the analysis of two compressible and incompressible flows, evolution equations of vorticity, acoustic and entropy modes are proposed for each flow region and mode couplings are assessed. For short times, perturbations are transferred from the external surface to the ablation front by diffusion and propagate as acoustic waves up to the shock wave. For long times, the shock region is governed by the free propagation of acoustic waves. A study of perturbations and associated sources allows us to identify strong mode couplings in the conduction and ablation regions. Moreover, the maximum instability depends on compressibility. Finally, a comparison with experiments of flows subjected to initial surface defects is initiated. (author)

  20. EFFECTIVENESS OF WASTE STABILIZATION PONDS IN REMOVAL OF LINEAR ALKYL BENZENE SALFONATE (LAS

    Ahmed. M. Abdel-Rahman

    2013-01-01

    Full Text Available Detergents contain synthetic or organic surface active agents called surfactants, which are derived from petroleum product precursors. They have the common property of lowering the surface tensions of water thus allowing dirt or grease adhered to various articles to be washed off. Linear alkyl benzene sulfonate (LAS is a most commonly used anionic surfactant. Discharge of raw or treated wastewater containing this chemical substance into the environment causes major public health and enviromental problems. In this study, samples were taken from raw wastewater and effluents of treatment ponds of Elzaraby waste stabilization ponds over a period of one year. The treated effluent is either discharged into surface waters or re-used in agricultural irrigation. The samples were analyzed according to the standard methods. The results obtained from the samples taken in different seasons showed that the highest overall removal efficiency of LAS was achieved in summer season (77%, and the least efficiency was observed in Winter season (55%, while the maximum overall efficiency of BOD5 was in summer (88% and minimum efficiency was (73% in winter season. The Dissolved oxygen concentrations along the pond series (DO ranged from 0.18 to 4.8 mg/l.

  1. Multiple Linear Regression Modeling To Predict the Stability of Polymer-Drug Solid Dispersions: Comparison of the Effects of Polymers and Manufacturing Methods on Solid Dispersion Stability.

    Fridgeirsdottir, Gudrun A; Harris, Robert J; Dryden, Ian L; Fischer, Peter M; Roberts, Clive J

    2018-03-29

    Solid dispersions can be a successful way to enhance the bioavailability of poorly soluble drugs. Here 60 solid dispersion formulations were produced using ten chemically diverse, neutral, poorly soluble drugs, three commonly used polymers, and two manufacturing techniques, spray-drying and melt extrusion. Each formulation underwent a six-month stability study at accelerated conditions, 40 °C and 75% relative humidity (RH). Significant differences in times to crystallization (onset of crystallization) were observed between both the different polymers and the two processing methods. Stability from zero days to over one year was observed. The extensive experimental data set obtained from this stability study was used to build multiple linear regression models to correlate physicochemical properties of the active pharmaceutical ingredients (API) with the stability data. The purpose of these models is to indicate which combination of processing method and polymer carrier is most likely to give a stable solid dispersion. Six quantitative mathematical multiple linear regression-based models were produced based on selection of the most influential independent physical and chemical parameters from a set of 33 possible factors, one model for each combination of polymer and processing method, with good predictability of stability. Three general rules are proposed from these models for the formulation development of suitably stable solid dispersions. Namely, increased stability is correlated with increased glass transition temperature ( T g ) of solid dispersions, as well as decreased number of H-bond donors and increased molecular flexibility (such as rotatable bonds and ring count) of the drug molecule.

  2. Hydrodynamic bearings

    Bonneau, Dominique; Souchet, Dominique

    2014-01-01

    This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the rheological models and the equations of lubrication. It also presents the numerical approaches used to solve the above equations by finite differences, finite volumes and finite elements methods.

  3. Hydrodynamic Lubrication

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 9. Hydrodynamic Lubrication Experiment with 'Floating' Drops. Jaywant H Arakeri K R Sreenivas. General Article Volume 1 Issue 9 September 1996 pp 51-58. Fulltext. Click here to view fulltext PDF. Permanent link:

  4. Theoretical hydrodynamics

    Milne-Thomson, L M

    2011-01-01

    This classic exposition of the mathematical theory of fluid motion is applicable to both hydrodynamics and aerodynamics. Based on vector methods and notation with their natural consequence in two dimensions - the complex variable - it offers more than 600 exercises and nearly 400 diagrams. Prerequisites include a knowledge of elementary calculus. 1968 edition.

  5. Hydrodynamic disperser

    Bulatov, A.I.; Chernov, V.S.; Prokopov, L.I.; Proselkov, Yu.M.; Tikhonov, Yu.P.

    1980-01-15

    A hydrodynamic disperser is suggested which contains a housing, slit nozzles installed on a circular base arranged opposite from each other, resonators secured opposite the nozzle and outlet sleeve. In order to improve the effectiveness of dispersion by throttling the flow, each resonator is made in the form of a crimped plate with crimpings that decrease in height in a direction towards the nozzle.

  6. On parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations

    Phan Thanh An; Phan Le Na; Ngo Quoc Chung

    2004-05-01

    We describe a practical implementation for finding parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations based on Korenevskij and Mitropolskij's sufficient condition and our sufficient conditions. Numerical results show that all of these sufficient conditions are crucial in the implementation. (author)

  7. Non-linear effects in electron cyclotron current drive applied for the stabilization of neoclassical tearing modes

    Ayten, B.; Westerhof, E.; ASDEX Upgrade team,

    2014-01-01

    Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived

  8. A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect

    Tian Chuan; Sun Di-Hua; Yang Shu-Hong

    2011-01-01

    We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world. Applying the linear stability theory, we obtain the linear stability condition of the model. Through nonlinear analysis, we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi-anticipation effect is considered. (interdisciplinary physics and related areas of science and technology)

  9. Large-scale perturbations of magnetohydrodynamic regimes linear and weakly nonlinear stability theory

    Zheligovsky, Vladislav

    2011-01-01

    New developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.

  10. Hydrodynamic cavitation for sonochemical effects.

    Moholkar, V S; Kumar, P S; Pandit, A B

    1999-03-01

    A comparative study of hydrodynamic and acoustic cavitation has been made on the basis of numerical solutions of the Rayleigh-Plesset equation. The bubble/cavity behaviour has been studied under both acoustic and hydrodynamic cavitation conditions. The effect of varying pressure fields on the collapse of the cavity (sinusoidal for acoustic and linear for hydrodynamic) and also on the latter's dynamic behaviour has been studied. The variations of parameters such as initial cavity size, intensity of the acoustic field and irradiation frequency in the case of acoustic cavitation, and initial cavity size, final recovery pressure and time for pressure recovery in the case of hydrodynamic cavitation, have been found to have significant effects on cavity/bubble dynamics. The simulations reveal that the bubble/cavity collapsing behaviour in the case of hydrodynamic cavitation is accompanied by a large number of pressure pulses of relatively smaller magnitude, compared with just one or two pulses under acoustic cavitation. It has been shown that hydrodynamic cavitation offers greater control over operating parameters and the resultant cavitation intensity. Finally, a brief summary of the experimental results on the oxidation of aqueous KI solution with a hydrodynamic cavitation set-up is given which supports the conclusion of this numerical study. The methodology presented allows one to manipulate and optimise of specific process, either physical or chemical.

  11. Railway Timetable Stability Analysis Using Stochastic Max-Plus Linear Systems

    Goverde, R.M.P.; Heidergott, B.; Merlet, G.

    2010-01-01

    Stability and robustness of a railway timetable are essential properties for punctual and reliable operations. Timetable performance evaluation is therefore an important aspect in the timetable design process. In particular, the stability and recoverability properties of a timetable with respect to

  12. Existence and Linear Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Oblateness

    Jagadish Singh

    2012-01-01

    Full Text Available This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.

  13. Adjustment of Adaptive Gain with Bounded Linear Stability Analysis to Improve Time-Delay Margin for Metrics-Driven Adaptive Control

    Bakhtiari-Nejad, Maryam; Nguyen, Nhan T.; Krishnakumar, Kalmanje Srinvas

    2009-01-01

    This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.

  14. Stability Analysis of Continuous-Time and Discrete-Time Quaternion-Valued Neural Networks With Linear Threshold Neurons.

    Chen, Xiaofeng; Song, Qiankun; Li, Zhongshan; Zhao, Zhenjiang; Liu, Yurong

    2018-07-01

    This paper addresses the problem of stability for continuous-time and discrete-time quaternion-valued neural networks (QVNNs) with linear threshold neurons. Applying the semidiscretization technique to the continuous-time QVNNs, the discrete-time analogs are obtained, which preserve the dynamical characteristics of their continuous-time counterparts. Via the plural decomposition method of quaternion, homeomorphic mapping theorem, as well as Lyapunov theorem, some sufficient conditions on the existence, uniqueness, and global asymptotical stability of the equilibrium point are derived for the continuous-time QVNNs and their discrete-time analogs, respectively. Furthermore, a uniform sufficient condition on the existence, uniqueness, and global asymptotical stability of the equilibrium point is obtained for both continuous-time QVNNs and their discrete-time version. Finally, two numerical examples are provided to substantiate the effectiveness of the proposed results.

  15. Energy principles for linear dissipative systems with application to resistive MHD stability

    Pletzer, A.

    1997-04-01

    A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand, differs from the Hamiltonian by being quadratic and by having a negative definite time derivative (positive power dissipation). The energy is a Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic (MHD) is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion D R <0 in the incompressible limit, whereas the tearing mode criterion Δ'<0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer. (author) 1 fig., 25 refs

  16. Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

    Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan

    2013-01-01

    We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method

  17. ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

    2008-01-01

    In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

  18. Combined influence of inertia, gravity, and surface tension on the linear stability of Newtonian fiber spinning

    Bechert, M.; Scheid, B.

    2017-11-01

    The draw resonance effect appears in fiber spinning processes if the ratio of take-up to inlet velocity, the so-called draw ratio, exceeds a critical value and manifests itself in steady oscillations of flow velocity and fiber diameter. We study the effect of surface tension on the draw resonance behavior of Newtonian fiber spinning in the presence of inertia and gravity. Utilizing an alternative scaling makes it possible to visualize the results in stability maps of highly practical relevance. The interplay of the destabilizing effect of surface tension and the stabilizing effects of inertia and gravity lead to nonmonotonic stability behavior and local stability maxima with respect to the dimensionless fluidity and the dimensionless inlet velocity. A region of unconditional instability caused by the influence of surface tension is found in addition to the region of unconditional stability caused by inertia, which was described in previous works [M. Bechert, D. W. Schubert, and B. Scheid, Eur. J. Mech B 52, 68 (2015), 10.1016/j.euromechflu.2015.02.005; Phys. Fluids 28, 024109 (2016), 10.1063/1.4941762]. Due to its importance for a particular group of fiber spinning applications, a viscous-gravity-surface-tension regime, i.e., negligible effect of inertia, is analyzed separately. The mechanism underlying the destabilizing effect of surface tension is discussed and established stability criteria are tested for validity in the presence of surface tension.

  19. Controllability of non-linear systems: generic singularities and their stability

    Davydov, Alexey A; Zakalyukin, Vladimir M

    2012-01-01

    This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.

  20. Spectrum of hydrodynamic volumes and sizes of macromolecules of linear polyelectrolytes versus their charge density in salt-free aqueous solutions.

    Pavlov, Georges M; Dommes, Olga A; Okatova, Olga V; Gavrilova, Irina I; Panarin, Evgenii F

    2018-04-18

    Molecular characteristics of statistical copolymers based on hydrophilic poly(N-methyl-N-vinylacetamide) have been monitored throughout the entire possible range of charge density from 1.5 to 39 mol%. Different trends in the dependence of intrinsic viscosity on the average charge density of polymer chains at minimal ionic strength were revealed. A new parameter, lqq/Abare, describing this behavior was proposed (lqq is the average distance between the neighboring charges along the chain, and Abare is the statistical segment length of a non-charged homologue). For polyelectrolyte chains, this parameter allows the regions of charge density values where electrostatic long-range or short-range interactions dominate to be indicated. Two homologous series of copolymers were characterized by methods of molecular hydrodynamics under conditions of suppressed charge effects. Intrinsic viscosity in salt-free solutions characterizing an individual macromolecule was estimated by a method proposed earlier [Pavlov et al., Russ. J. Appl. Chem., 2006, 79, 1407-1412].

  1. Theoretical explanation of present mirror experiments and linear stability of larger scaled machines

    Berk, H.L.; Baldwin, D.E.; Cutler, T.A.; Lodestro, L.L.; Maron, N.; Pearlstein, L.D.; Rognlien, T.D.; Stewart, J.J.; Watson, D.C.

    1976-01-01

    A quasilinear model for the evolution of the 2XIIB mirror experiment is presented and shown to reproduce the time evolution of the experiment. From quasilinear theory it follows that the energy lifetime is the Spitzer electron drag time for T/sub e/ approximately less than 0.1T/sub i/. By computing the stability boundary of the DCLC mode, with warm plasma stabilization, the electron temperature is predicted as a function of radial scale length. In addition, the effect of finite length corrections to the Alfven cyclotron mode is assessed

  2. Supernova hydrodynamics

    Colgate, S.A.

    1981-01-01

    The explosion of a star supernova occurs at the end of its evolution when the nuclear fuel in its core is almost, or completely, consumed. The star may explode due to a small residual thermonuclear detonation, type I SN or it may collapse, type I and type II SN leaving a neutron star remnant. The type I progenitor should be thought to be an old accreting white dwarf, 1.4 M/sub theta/, with a close companion star. A type II SN is thought to be a massive young star 6 to 10 M/sub theta/. The mechanism of explosion is still a challenge to our ability to model the most extreme conditions of matter and hydrodynamics that occur presently and excessively in the universe. 39 references

  3. Physical hydrodynamics

    Guyon, Etienne; Petit, Luc; Mitescu, Catalin D

    2015-01-01

    This new edition is an enriched version of the textbook of fluid dynamics published more than 10 years ago. It retains the same physically oriented pedagogical perspective. This book emphasizes, as in the first edition, experimental inductive approaches and relies on the study of the mechanisms at play and on dimensional analysis rather than more formal approaches found in many classical textbooks in the field. The need for a completely new version also originated from the increase, over the last few decades, of the cross-overs between the mechanical and physical approaches, as is visible in international meetings and joint projects. Hydrodynamics is more widely linked today to other fields of experimental sciences: materials, environment, life sciences and earth sciences, as well as engineering sciences.

  4. Introduction to hydrodynamics

    Wilkins, M.L.

    1979-01-01

    Various aspects of hydrodynamics and elastic--plastic flow are introduced for the purpose of defining hydrodynamic terms and explaining what some of the important hydrodynamic concepts are. The first part covers hydrodynamic theory; and discussed fundamental hydrodynamic equations, discontinuities, and shock, detonation, and elastic--plastic waves. The second part deals with applications of hydrodynamic theory to material equations of state, spall, Taylor instabilities, and detonation pressure measurements

  5. Input-to-State Stabilizing MPC for Neutrally Stable Linear Systems subject to Input Constraints

    Kim, Jung-Su; Yoon, Tae-Woong; Jadbabaie, Ali; Persis, Claudio De

    2004-01-01

    MPC(Model Predictive Control) is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed

  6. On the Linear Stability of the Fifth-Order WENO Discretization

    Motamed, Mohammad; Macdonald, Colin B.; Ruuth, Steven J.

    2010-01-01

    , the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC

  7. Numerical simulations and linear stability analysis of a boundary layer developed on wavy surfaces

    Siconolfi, Lorenzo; Camarri, Simone; Fransson, Jens H. M.

    2015-11-01

    The development of passive methods leading to a laminar to turbulent transition delay in a boundary layer (BL) is a topic of great interest both for applications and academic research. In literature it has been shown that a proper and stable spanwise velocity modulation can reduce the growth rate of Tollmien-Schlichting (TS) waves and delay transition. In this study, we investigate numerically the possibility of obtaining a stabilizing effect of the TS waves through the use of a spanwise sinusoidal modulation of a flat plate. This type of control has been already successfully investigated experimentally. An extensive set of direct numerical simulations is carried out to study the evolution of a BL flow developed on wavy surfaces with different geometric characteristics, and the results will be presented here. Moreover, since this configuration is characterized by a slowly-varying flow field in streamwise direction, a local stability analysis is applied to define the neutral stability curves for the BL flow controlled by this type of wall modifications. These results give the possibility of investigating this control strategy and understanding the effect of the free parameters on the stabilization mechanism.

  8. Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

    Bonito, Andrea

    2013-10-03

    We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.

  9. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....

  10. Hydrodynamic instabilities in inertial fusion

    Hoffman, N.M.

    1994-01-01

    This report discusses topics on hydrodynamics instabilities in inertial confinement: linear analysis of Rayleigh-Taylor instability; ablation-surface instability; bubble rise in late-stage Rayleigh-Taylor instability; and saturation and multimode interactions in intermediate-stage Rayleigh-Taylor instability

  11. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

    2016-09-15

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  12. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A.

    2016-09-01

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  13. Recent results on stability and response bounds of linear systems - a review

    Pommer, Christian; Kliem, Wolfhard

    2006-01-01

    The literature on linear systems emerging from second order differential equations is extensive because such systems are ubiquitous in modeling, particularly modeling of mechanical systems. This paper offers an overview of some of the recent research in this field, in particular on the subject...

  14. Thermo-hydrodynamic lubrication in hydrodynamic bearings

    Bonneau, Dominique; Souchet, Dominique

    2014-01-01

    This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the thermo-hydrodynamic and the thermo-elasto-hydrodynamic lubrication. The algorithms are methodically detailed and each section is thoroughly illustrated.

  15. STABILITY OF LINEAR MULTIAGENT SCALAR SYSTEMS AND ITS DEPENDENCE ON CONNECTIVITY GRAPH

    S. I. Tomashevich

    2014-03-01

    Full Text Available Multiagent systems are now finding increasingly wide applications in various engineering fields such as energy, transportation, robotics, aviation and others. There are two main aspects to be focused on when organizing multiagent systems: the dynamics of the agents themselves and the ways of their interaction. This interaction is determined by the structure of information connections between agents. Thus, there are several key points of multiagent systems study: the dynamics of individual agents and shape of the information graph. Formation dynamics, in general, is determined by a set of properties of agents and connectivity graph. The paper deals with the relationship between dynamics of agents and Laplace matrix, which is used to set the graph connections. The present research is based on the results given in the known paper by A. Fax and R. Murray (IEEE Trans. AC, 2004. An illustrative example is given, and the application problem of studying the formation dynamics consisting of the group of quadrocopters is presented. Information exchange between agents is determined in the paper by means of the conventional set of graphs. The paper presents an interpretation of the stability conditions and the method of system performance improvement based on these conditions. Motion of quadrocopters group along the flight height is used as an example for methodology application. The simulation results demonstrate the basic dependencies between the information graph shape (and, consequently, the eigenvalues of the Laplacian, which describes this graph and formation stability. Simulation and consideration of Nyquist diagram connection with the key points give an indication of the system stability and take steps to change the control laws. Necessary conditions for the formation stability are obtained on the basis of this research method. Research result makes it possible to create local control laws for agents to ensure the stability of motion in the selected

  16. Numerical simulation and global linear stability analysis of low-Re flow past a heated circular cylinder

    Zhang, Wei

    2016-03-31

    We perform two-dimensional unsteady Navier-Stokes simulation and global linear stability analysis of flow past a heated circular cylinder to investigate the effect of aided buoyancy on the stabilization of the flow. The Reynolds number of the incoming flow is fixed at 100, and the Richardson number characterizing the buoyancy is varied from 0.00 (buoyancy-free case) to 0.10 at which the flow is still unsteady. We investigate the effect of aided buoyancy in stabilizing the wake flow, identify the temporal and spatial characteristics of the growth of the perturbation, and quantify the contributions from various terms comprising the perturbed kinetic energy budget. Numerical results reveal that the increasing Ri decreases the fluctuation magnitude of the characteristic quantities monotonically, and the momentum deficit in the wake flow decays rapidly so that the flow velocity recovers to that of the free-stream; the strain on the wake flow is reduced in the region where the perturbation is the most greatly amplified. Global stability analysis shows that the temporal growth rate of the perturbation decreases monotonically with Ri, reflecting the stabilization of the flow due to aided buoyancy. The perturbation grows most significantly in the free shear layer separated from the cylinder. As Ri increases, the location of maximum perturbation growth moves closer to the cylinder and the perturbation decays more rapidly in the far wake. The introduction of the aided buoyancy alters the base flow, and destabilizes the near wake shear layer mainly through the strain-induced transfer term and the pressure term of the perturbed kinetic energy, whereas the flow is stabilized in the far wake as the strain is alleviated. © 2016 Elsevier Ltd. All rights reserved.

  17. Numerical simulation and global linear stability analysis of low-Re flow past a heated circular cylinder

    Zhang, Wei; Samtaney, Ravi

    2016-01-01

    We perform two-dimensional unsteady Navier-Stokes simulation and global linear stability analysis of flow past a heated circular cylinder to investigate the effect of aided buoyancy on the stabilization of the flow. The Reynolds number of the incoming flow is fixed at 100, and the Richardson number characterizing the buoyancy is varied from 0.00 (buoyancy-free case) to 0.10 at which the flow is still unsteady. We investigate the effect of aided buoyancy in stabilizing the wake flow, identify the temporal and spatial characteristics of the growth of the perturbation, and quantify the contributions from various terms comprising the perturbed kinetic energy budget. Numerical results reveal that the increasing Ri decreases the fluctuation magnitude of the characteristic quantities monotonically, and the momentum deficit in the wake flow decays rapidly so that the flow velocity recovers to that of the free-stream; the strain on the wake flow is reduced in the region where the perturbation is the most greatly amplified. Global stability analysis shows that the temporal growth rate of the perturbation decreases monotonically with Ri, reflecting the stabilization of the flow due to aided buoyancy. The perturbation grows most significantly in the free shear layer separated from the cylinder. As Ri increases, the location of maximum perturbation growth moves closer to the cylinder and the perturbation decays more rapidly in the far wake. The introduction of the aided buoyancy alters the base flow, and destabilizes the near wake shear layer mainly through the strain-induced transfer term and the pressure term of the perturbed kinetic energy, whereas the flow is stabilized in the far wake as the strain is alleviated. © 2016 Elsevier Ltd. All rights reserved.

  18. Linear stability theory as an early warning sign for transitions in high dimensional complex systems

    Piovani, Duccio; Grujić, Jelena; Jensen, Henrik Jeldtoft

    2016-01-01

    We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently. (paper)

  19. Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

    S. Alonso-Quesada

    2010-01-01

    Full Text Available This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant (LTI continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.

  20. Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2

    Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

    1980-07-01

    The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt

  1. Stability of a mobile electron linear accelerator system for intraoperative radiation therapy

    Beddar, A. Sam

    2005-01-01

    The flexibility of mobile electron accelerators, which are designed to be transported to an operating room and plugged into a normal 3-phase outlet, make them ideal for use in intraoperative radiation therapy. However, their transportability may cause trepidation among potential users, who may question the stability of such an accelerator over a period of use. In order to address this issue, we have studied the short-term stability of the Mobetron system over 20 daily quality assurance trials. Variations in output generally varied within ±2% for the four energies produced by the unit (4, 6, 9, and 12 MeV) and changes in energy produced an equivalent shift of less than 1 mm on the depth-dose curve. Hours of inactivity, with the Mobetron powered on for use either throughout the day or overnight, led to variations in output of about 1%. Finally, we have tested the long-term stability of the absolute dose output of the Mobetron, which showed a change of about 1% per year

  2. Linear Stability Analysis of Laminar Premixed Fuel-Rich Double-Spray Flames

    Noam Weinberg

    2014-03-01

    Full Text Available This paper considers the stability of a double-spray premixed flame formed when both fuel and oxidizer are initially present in the form of sprays of evaporating liquid droplets. To simplify the inherent complexity that characterizes the analytic solution of multi-phase combustion processes, the analysis is restricted to fuel-rich laminar premixed double-spray flames, and assumes a single-step global chemical reaction mechanism. Steady-state solutions are obtained and the sensitivity of the flame temperature and the flame propagating velocity to the initial liquid fuel and/or oxidizer loads are established. The stability analysis revealed an increased proneness to cellular instability induced by the presence of the two sprays, and for the fuel-rich case considered here the influence of the liquid oxidizer was found to be more pronounced than that of the liquid fuel. Similar effects were noted for the neutral pulsating stability boundaries. The impact of unequal latent heats of vaporization is also investigated and found to be in keeping with the destabilizing influence of heat loss due to droplet evaporation. It should be noted that as far as the authors are aware no experimental evidence is available for (at least validation of the predictions. However, they do concur in a general and reasonable fashion with independent experimental evidence in the literature of the behavior of single fuel spray laminar premixed flames.

  3. Sufficient condition for the linearization stability of N = 1 supergravity: A preliminary report

    Bao, D.

    1984-01-01

    This paper outlines how the methods developed by Fischer, Marsden, and Moncrief (A. Fischer and J. Marsden, ''Isolated Gravitating Systems in General Relativity,'' (J. Ehlers, Ed.), Proceedings of the International School of Physics Enrico Fermi Course XVII, North-Holland, Amsterdam, 1979; A. Fischer, J. Marsden, and V. Moncrief, Ann. Inst. Henri Poincare 33 (1980), 147-194) for general relativity are being used to show that classical N = 1 supergravity, as a non-linear system of partial differential equtions, is linearization stable at any solution which lacks Killing symmetry. It is assumed (for convenience) throughout that the underlying spacetime is topologically Σ 0 x R, where Σ 0 is a compact, spacelike, and boundaryless 3-dimensional hypersurface

  4. Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

    M. de la Sen

    2010-01-01

    Full Text Available This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that (q+1 polytopic parameterizations are considered for a system with q delays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

  5. Hydrodynamic dispersion

    Pryce, M.H.L.

    1985-01-01

    A dominant mechanism contributing to hydrodynamic dispersion in fluid flow through rocks is variation of travel speeds within the channels carrying the fluid, whether these be interstices between grains, in granular rocks, or cracks in fractured crystalline rocks. The complex interconnections of the channels ensure a mixing of those parts of the fluid which travel more slowly and those which travel faster. On a macroscopic scale this can be treated statistically in terms of the distribution of times taken by a particle of fluid to move from one surface of constant hydraulic potential to another, lower, potential. The distributions in the individual channels are such that very long travel times make a very important contribution. Indeed, while the mean travel time is related to distance by a well-defined transport speed, the mean square is effectively infinite. This results in an asymmetrical plume which differs markedly from a gaussian shape. The distribution of microscopic travel times is related to the distribution of apertures in the interstices, or in the microcracks, which in turn are affected in a complex way by the stresses acting on the rock matrix

  6. New exponential stability conditions for linear delayed systems of differential equations

    Leonid Berezansky

    2016-08-01

    where $t\\ge 0$, $m$ and $r_{ij}$, $i,j=1,\\dots,m$ are natural numbers, $a_{ij}^{k}\\colon [0,\\infty\\to\\mathbb{R}$ are measurable coefficients, and $h_{ij}^{k}\\colon [0,\\infty\\to\\mathbb{R}$ are measurable delays. The progress was achieved by using a new technique making it possible to replace the constant $1$ by the constant $1+{1}/{\\mathrm{e}}$ on the right-hand sides of crucial inequalities ensuring exponential stability.

  7. Stability of the particle transverse motion in an electron linear accelerator with beam recirculation

    Volodin, V.A.

    1979-01-01

    Conditions, under which beam transverse instabilities appear in the electron linear accelerator (ELA) with a double particle acceleration due to excitation of asymmetric stray waves in the accelerating waveguide, and their peculiarities have been investigated. It is shown that in the ELA with beam recirculation the conditions under which the beam transverse instability appears can be determined with the help of the ''interaction function'' which depends on both the accelerating structure and the focusing in the beam transport channel. Comparison is made with characteristics of this phenomenon in conventional ELA, and possible reasons for the decrease of a starting current in ELA with recirculation are shown

  8. Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

    Yoshioka, Masahiko

    2002-01-01

    We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatiotemporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatiotemporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast α function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with α function is reduced to the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision

  9. Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity

    Rand, J. L.; Wakefield, D. S.

    Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may

  10. Linear Aspects of Stability in Flow Induced Oscillations of Cantilever Pipes: Application of a Popular Heuristic Algorithm

    Hebbar, Ullhas; Krishnan, Abilash; Kadoli, Ravikiran

    2017-11-01

    This work studied linear aspects of flow induced oscillations in cantilever pipes, with an emphasis on the numerical method of solution adopted for the system of governing equations. The complex frequencies of vibration of the different characteristic modes of the system were computed as a function of the flow velocity, wherein multi-variable minimization was performed using the popular Nelder-Mead heuristic algorithm. Results for a canonical fluid-to-pipe mass ratio (β) were validated with literature, and the evolution of frequencies was studied for different mass ratios. Additionally, the numerical scheme was implemented to compute critical conditions of stability for the cantilever system as a function of β. Finally, interesting aspects of the dynamics of the system were analyzed: the supposed `mode exchange' behavior, and an explanation for discontinuities observed in the critical conditions plotted as a function of β. In conclusion, the heuristic optimization based solution used in this study can be used to analyze various aspects of linear stability in pipes conveying fluid. Part of the submitted work was completed at the author's previous affiliation - National Institute of Technology Karnataka, India.

  11. Mix and hydrodynamic instabilities on NIF

    Smalyuk, V. A.; Robey, H. F.; Casey, D. T.; Clark, D. S.; Döppner, T.; Haan, S. W.; Hammel, B. A.; MacPhee, A. G.; Martinez, D.; Milovich, J. L.; Peterson, J. L.; Pickworth, L.; Pino, J. E.; Raman, K.; Tipton, R.; Weber, C. R.; Baker, K. L.; Bachmann, B.; Berzak Hopkins, L. F.; Bond, E.; Caggiano, J. A.; Callahan, D. A.; Celliers, P. M.; Cerjan, C.; Dixit, S. N.; Edwards, M. J.; Felker, S.; Field, J. E.; Fittinghoff, D. N.; Gharibyan, N.; Grim, G. P.; Hamza, A. V.; Hatarik, R.; Hohenberger, M.; Hsing, W. W.; Hurricane, O. A.; Jancaitis, K. S.; Jones, O. S.; Khan, S.; Kroll, J. J.; Lafortune, K. N.; Landen, O. L.; Ma, T.; MacGowan, B. J.; Masse, L.; Moore, A. S.; Nagel, S. R.; Nikroo, A.; Pak, A.; Patel, P. K.; Remington, B. A.; Sayre, D. B.; Spears, B. K.; Stadermann, M.; Tommasini, R.; Widmayer, C. C.; Yeamans, C. B.; Crippen, J.; Farrell, M.; Giraldez, E.; Rice, N.; Wilde, C. H.; Volegov, P. L.; Gatu Johnson, M.

    2017-06-01

    Several new platforms have been developed to experimentally measure hydrodynamic instabilities in all phases of indirect-drive, inertial confinement fusion implosions on National Ignition Facility. At the ablation front, instability growth of pre-imposed modulations was measured with a face-on, x-ray radiography platform in the linear regime using the Hydrodynamic Growth Radiography (HGR) platform. Modulation growth of "native roughness" modulations and engineering features (fill tubes and capsule support membranes) were measured in conditions relevant to layered DT implosions. A new experimental platform was developed to measure instability growth at the ablator-ice interface. In the deceleration phase of implosions, several experimental platforms were developed to measure both low-mode asymmetries and high-mode perturbations near peak compression with x-ray and nuclear techniques. In one innovative technique, the self-emission from the hot spot was enhanced with argon dopant to "self-backlight" the shell in-flight. To stabilize instability growth, new "adiabat-shaping" techniques were developed using the HGR platform and applied in layered DT implosions.

  12. Standing Wave Linear Accelerators: An Investigation of the Fundamental Field Stability and Tuning Characteristics

    2002-01-01

    The first accelerators were designed as a tool in high-energy particle physics. Their development has given rise to numerous applications in industry, such as materials processing, sterilization, food preservation, and radiopharmaceutical product generation (Barbalat, 1994). Modern day linear accelerators for particle physics accelerate multiple bunches of electrons and positrons up to 50 GeV. Accelerators of the next generation, such as the Next Linear Collider (NLC), aim to accelerate the bunches initially to a center of mass of 500GeV and later to 1.5 TeV (Decking 2001, Miyamoto 2002, Phinney 2002). The NLC will operate under gradient fields on the order of 70 MV/m (Phinney, 2002). For all accelerators, two issues are fundamental for their construction: maximizing the efficiency of acceleration while, at the same time, preserving the luminosity of the beam. These issues are critically important in the design of the NLC. A linear accelerator operates as follows: An electron gun fires electrons into a structure that bunches the electrons and tightly focuses the beam. At the same time, a radiofrequency wave is fed into the accelerating structure. The electron bunches enter the accelerating structure in phase with the crest of the radiofrequency wave in order to achieve maximum energy. There are two principal types of accelerating structures: traveling wave (TW) and standing wave (SW). The electromagnetic wave in a TW structure travels in one direction; the electromagnetic wave in a SW structure travels in two directions. Many TW structures have been designed for the NLC, but recent experiments indicate that TW structures suffer from electrical breakdown at high gradients (Miller et. al., 2001). To address this problem, SW structures are being considered as the alternative for the NLC (Jones and Miller et. al., 2002). The input power required for an accelerating cavity increases with the length of the cavity (Miller et. al., 2001). Since SW structures can be made

  13. Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null

    Kim, J.S.

    1984-01-01

    Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null

  14. Assessment of beam stability of high energy and low energy Varian medical linear accelerators

    Jayesh, K.; Mohan, R.; Joshi, R.C.; Ganesh, T.; Hegazy, M.; Oubaye, A.J.; AI Idrisi, Maha

    2008-01-01

    An accurate measurement of the dose delivered to the tumor in external beam radiotherapy is one of the primary responsibilities of a medical physicist. In general, such measurements have been based on the application of a dosimetry protocol and quality assurance procedures. Clinically one must be able to assess the beam quality, flatness and symmetry and variation in the output on daily basis. Flatness and symmetry are the main parameters for determining the pattern of a photon and electron beam produced by linear accelerators. The quality assurance in routine clinical practice of radiotherapy and consequently the treatment-outcome depends definitely on the physical parameters of treatment-delivery. Several recommendations from national and international associations are reported to define the limits for the beam parameters. The review of literature and various reports on quality assurance in radiotherapy show that for flatness, symmetry and output constancy the optimal level of deviation should be within ±3%

  15. Effect of liner non-uniformity on plasma instabilities in an inverse Z-pinch magnetized target fusion system: liner-on-plasma simulations and comparison with linear stability analysis

    Subhash, P V; Madhavan, S; Chaturvedi, S

    2008-01-01

    Two-dimensional (2D) magneto-hydrodynamic (MHD) liner-on-plasma computations have been performed to study the growth of instabilities in a magnetized target fusion system involving the cylindrical compression of an inverse Z-pinch target plasma by a metallic liner. The growth of modes in the plasma can be divided into two phases. During the first phase, the plasma continues to be Kadomtsev stable. The dominant mode in the liner instability is imposed upon the plasma in the form of a growing perturbation. This mode further transfers part of its energy to its harmonics. During the second phase, however, non-uniform implosion of the liner leads to axial variations in plasma quantities near the liner-plasma interface, such that certain regions of the plasma locally violate the Kadomtsev criteria. Further growth ofthe plasma modes is then due to plasma instability. The above numerical study has been complemented with a linear stability analysis for the plasma, the boundary conditions for this analysis being obtained from the liner-on-plasma simulation. The stability of axisymmetric modes in the first phase is found to satisfy the Kadomtsev condition Q 0 1 modes, using equilibrium profiles from the 2D MHD study, shows that their growth rates can exceed those for m=0 by as much as an order of magnitude

  16. Linear stability of resistive MHD modes: axisymmetric toroidal computation of the outer region matching data

    Pletzer, A.; Bondeson, A.; Dewar, R.L.

    1993-11-01

    The quest to determine accurately the stability of tearing and resistive interchange modes in two-dimensional toroidal geometry led to the development of the PEST-3 code, which is based on solving the singular, zero-frequency ideal MHD equation in the plasma bulk and determining the outer data Δ', Γ' and A' needed to match the outer region solutions to those arising in the inner layers. No assumption regarding the aspect ratio, the number of rational surfaces or the pressure are made a priori. This approach is numerically less demanding than solving the full set of resistive equations, and has the major advantage of non-MHD theories of the non-ideal layers. Good convergence is ensured by the variational Galerkin scheme used to compute the outer matching data. To validate the code, we focus on the growth rate calculations of resistive kink modes which are reproduced in good agreement with those obtained by the full resistive MHD code MARS. (author) 11 figs., 27 refs

  17. Linear stability of toroidal Alfvén eigenmodes in the Chinese Fusion Engineering Test Reactor

    Yang, Wenjun [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); University of Science and Technology of China, Hefei, Anhui 230026 (China); Li, Guoqiang, E-mail: ligq@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Hu, Youjun; Gao, Xiang [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China)

    2017-01-15

    The Chinese Fusion Engineering Test Reactor (CFETR) is under design. It aims to fill the gaps between ITER and DEMO. In the reactor, the deuterium-tritium fusion reaction and the auxiliary heating will generate a lot of energetic particles. It is possible that these energetic particles will drive toroidal Alfvén eigenmode (TAE) instabilities under the conditions of CFETR plasma parameters. These instabilities can result in energetic particles redistribution or loss, so it’s vital to study TAE instabilities in CFETR. The aim of this paper is to study the possibility of reducing TAE instabilities by changing safety factor profiles in CFETR. NOVA and NOVA-K codes are used to study TAE stability. The equilibria are constructed using the CORSICA code. Safety factor profiles are selected as the three typical profiles of ITER scenarios. For the three different safety factor profiles, we use NOVA to scan and calculate their continuum spectrum and eigenmode structures, then use NOVA-K to calculate the different damping and driving mechanisms for different toroidal mode numbers. The numerical calculations show that if the safety factor profiles are chosen appropriately, then all the TAEs can be stable. Thus, it’s possible to reduce the TAE instabilities by changing safety factor profiles in CFETR. We also scan the temperature and density profiles to see their effects on the TAE instabilities. It shows that the TAE instabilities keep unchanged for a wide range of profiles.

  18. Geometric method for stability of non-linear elastic thin shells

    Ivanova, Jordanka

    2002-01-01

    PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...

  19. Simulation and characterization of the RF system and global stability analysis at the REGAE linear electron accelerator

    Mayet, Frank

    2012-12-01

    LAOLA (LAboratory for Laser- and beam-driven plasma Acceleration), is a collaboration between groups from DESY and the University of Hamburg. Its mission is to complement basic research in the relatively new field of plasma wakefield acceleration (PWA) by an explicit combination with DESY's conventional, modern accelerators. The linear electron accelerator REGAE is designed to produce sub 10 fs low charge electron bunches with ultra-low emittance at a repetition rate of 50 Hz. The planned experiments include femtosecond electron diffraction (R.J. Dwayne Miller), as well as the probing of laser induced plasma wakefields with well characterized bunches (LAOLA). They all require high bunch time of flight stability down to 10 fs. The REGAE machine consists of two RF cavities, both fed by a single klystron. While the first one - the gun cavity - is used for acceleration of the electrons, the second one - the buncher cavity - can be used to reduce the electron bunch length. This scheme only works for a specific RF phase relation between the two cavities. This thesis is split into two parts. In the first one the implications of the unique two cavity design on day-to-day machine operation are analyzed. To this end an analytical model of the RF system is developed, which is necessary for understanding how to individually adjust the cavity phases. In the second part the influence of the setup on time of flight stability is discussed with an emphasis on phase jitter compensation. RF phase stability measurements reveal that the current machine setup allows for a time of flight stability down to 50 fs right after the gun.

  20. Simulation and characterization of the RF system and global stability analysis at the REGAE linear electron accelerator

    Mayet, Frank

    2012-12-15

    LAOLA (LAboratory for Laser- and beam-driven plasma Acceleration), is a collaboration between groups from DESY and the University of Hamburg. Its mission is to complement basic research in the relatively new field of plasma wakefield acceleration (PWA) by an explicit combination with DESY's conventional, modern accelerators. The linear electron accelerator REGAE is designed to produce sub 10 fs low charge electron bunches with ultra-low emittance at a repetition rate of 50 Hz. The planned experiments include femtosecond electron diffraction (R.J. Dwayne Miller), as well as the probing of laser induced plasma wakefields with well characterized bunches (LAOLA). They all require high bunch time of flight stability down to 10 fs. The REGAE machine consists of two RF cavities, both fed by a single klystron. While the first one - the gun cavity - is used for acceleration of the electrons, the second one - the buncher cavity - can be used to reduce the electron bunch length. This scheme only works for a specific RF phase relation between the two cavities. This thesis is split into two parts. In the first one the implications of the unique two cavity design on day-to-day machine operation are analyzed. To this end an analytical model of the RF system is developed, which is necessary for understanding how to individually adjust the cavity phases. In the second part the influence of the setup on time of flight stability is discussed with an emphasis on phase jitter compensation. RF phase stability measurements reveal that the current machine setup allows for a time of flight stability down to 50 fs right after the gun.

  1. Environmental protection stability of river bed and banks using convex, concave, and linear bed sills.

    Keshavarzi, Alireza; Noori, Lila Khaje

    2010-12-01

    River bed scourings are a major environmental problem for fish and aquatic habitat resources. In this study, to prevent river bed and banks from scouring, different types of bed sills including convex, concave and linear patterns were installed in a movable channel bed in a laboratory flume. The bed sills were tested with nine different arrangements and under different flow conditions. To find the most effective bed sill pattern, the scouring depth was measured downstream of the bed sill for a long experimental duration. The scour depth was measured at the middle and at the end of each experimental test for different ratios of the arch radius to the channel width [r/w]. The experimental results indicated that the convex pattern with r/w=0.35 produced minimum bed scouring depth at the center line whereas the concave pattern with r/w=0.23 produced the minimum scour depth at the wall banks. Therefore, the convex pattern was the most effective configuration for prevention of scouring at the center line of the river while the concave pattern was very effective to prevent scouring at the river banks. These findings can be suggested to be used in practical applications.

  2. Effective Surfactants Blend Concentration Determination for O/W Emulsion Stabilization by Two Nonionic Surfactants by Simple Linear Regression.

    Hassan, A K

    2015-01-01

    In this work, O/W emulsion sets were prepared by using different concentrations of two nonionic surfactants. The two surfactants, tween 80(HLB=15.0) and span 80(HLB=4.3) were used in a fixed proportions equal to 0.55:0.45 respectively. HLB value of the surfactants blends were fixed at 10.185. The surfactants blend concentration is starting from 3% up to 19%. For each O/W emulsion set the conductivity was measured at room temperature (25±2°), 40, 50, 60, 70 and 80°. Applying the simple linear regression least squares method statistical analysis to the temperature-conductivity obtained data determines the effective surfactants blend concentration required for preparing the most stable O/W emulsion. These results were confirmed by applying the physical stability centrifugation testing and the phase inversion temperature range measurements. The results indicated that, the relation which represents the most stable O/W emulsion has the strongest direct linear relationship between temperature and conductivity. This relationship is linear up to 80°. This work proves that, the most stable O/W emulsion is determined via the determination of the maximum R² value by applying of the simple linear regression least squares method to the temperature-conductivity obtained data up to 80°, in addition to, the true maximum slope is represented by the equation which has the maximum R² value. Because the conditions would be changed in a more complex formulation, the method of the determination of the effective surfactants blend concentration was verified by applying it for more complex formulations of 2% O/W miconazole nitrate cream and the results indicate its reproducibility.

  3. Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring

    El-Nashar, Hassan F.

    2017-06-01

    We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.

  4. Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement

    Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.

    2018-03-01

    In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.

  5. Towards the prediction of multiple necking during dynamic extension of round bar: linear stability approach versus finite element calculations

    Maï, S El; Petit, J; Mercier, S; Molinari, A

    2014-01-01

    The fragmentation of structures subject to dynamic conditions is a matter of interest for civil industries as well as for Defence institutions. Dynamic expansions of structures, such as cylinders or rings, have been performed to obtain crucial information on fragment distributions. Many authors have proposed to capture by FEA the experimental distribution of fragment size by introducing in the FE model a perturbation. Stability and bifurcation analyses have also been proposed to describe the evolution of the perturbation growth rate. In the proposed contribution, the multiple necking of a round bar in dynamic tensile loading is analysed by the FE method. A perturbation on the initial flow stress is introduced in the numerical model to trigger instabilities. The onset time and the dominant mode of necking have been characterized precisely and showed power law evolutions, with the loading velocities and moderately with the amplitudes and the cell sizes of the perturbations. In the second part of the paper, the development of linear stability analysis and the use of salient criteria in terms of the growth rate of perturbations enabled comparisons with the numerical results. A good correlation in terms of onset time of instabilities and of number of necks is shown.

  6. In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

    Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

    2014-01-01

    Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

  7. Hydrodynamic potentials for the micropolar Navier-Stokes problem

    Martynenko, M.D.; Dimian, M.

    1995-01-01

    An integral representation of linear and angular velocities and pressure for the description of linear stationary flows of micropolar viscous liquid media is obtained, and on its basis hydrodynamic potentials for the micropolar Navier-Stokes problem are introduced

  8. Laser driven hydrodynamic instability experiments

    Remington, B.A.; Weber, S.V.; Haan, S.W.; Kilkenny, J.D.; Glendinning, S.G.; Wallace, R.J.; Goldstein, W.H.; Wilson, B.G.; Nash, J.K.

    1993-01-01

    An extensive series of experiments has been conducted on the Nova laser to measure hydrodynamic instabilities in planar foils accelerated by x-ray ablation. Single mode experiments allow a measurement of the fundamental growth rates from the linear well into the nonlinear regime. Two-mode foils allow a first direct observation of mode coupling. Surface-finish experiments allow a measurement of the evolution of a broad spectrum of random initial modes

  9. Numerical Hydrodynamics in General Relativity

    Font José A.

    2003-01-01

    Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.

  10. Stability and suppression of turbulence in relaxing molecular gas flows

    Grigoryev, Yurii N

    2017-01-01

    This book presents an in-depth systematic investigation of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The work describes the theoretical foundations of a new way to control stability and laminar turbulent transitions in aerodynamic flows. It develops hydrodynamic models for describing thermal nonequilibrium gas flows which allow the consideration of suppression of inviscid acoustic waves in 2D shear flows. Then, nonlinear evolution of large-scale vortices and Kelvin-Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both linear and nonlinear classical energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of the book is to show the new dissipative effect, which can be used for flo...

  11. Linearity stabilizes discrete breathers

    themselves and with the boundaries leading to the eventual formation of an ... explored where these fascinating entities are being studied as, for example, ... Josephson-junction arrays, layered silicates, micromechanical cantilever ... velocities at late times (an expected result based on the Central Limit Theorem) and the.

  12. Existence and Stability of the Periodic Solution with an Interior Transitional Layer in the Problem with a Weak Linear Advection

    Nikolay N. Nefedov

    2018-01-01

    Full Text Available In the paper, we study a singularly perturbed periodic in time problem for the parabolic reaction-advection-diffusion equation with a weak linear advection. The case of the reactive term in the form of a cubic nonlinearity is considered. On the basis of already known results, a more general formulation of the problem is investigated, with weaker sufficient conditions for the existence of a solution with an internal transition layer to be provided than in previous studies. For convenience, the known results are given, which ensure the fulfillment of the existence theorem of the contrast structure. The justification for the existence of a solution with an internal transition layer is based on the use of an asymptotic method of differential inequalities based on the modification of the terms of the constructed asymptotic expansion. Further, sufficient conditions are established to fulfill these requirements, and they have simple and concise formulations in the form of the algebraic equation w(x0,t = 0 and the condition wx(x0,t < 0, which is essentially a condition of simplicity of the root x0(t and ensuring the stability of the solution found. The function w is a function of the known functions appearing in the reactive and advective terms of the original problem. The equation w(x0,t = 0 is a problem for finding the zero approximation x0(t to determine the localization region of the inner transition layer. In addition, the asymptotic Lyapunov stability of the found periodic solution is investigated, based on the application of the so-called compressible barrier method. The main result of the paper is formulated as a theorem. 

  13. BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

    Zhang, Wei

    2016-04-04

    We perform BiGlobal linear stability analysis on flow past a NACA0012 airfoil at 16° angle of attack and Reynolds number ranging from 400 to 1000. The steady-state two-dimensional base flows are computed using a well-tested finite difference code in combination with the selective frequency damping method. The base flow is characterized by two asymmetric recirculation bubbles downstream of the airfoil whose streamwise extent and the maximum reverse flow velocity increase with the Reynolds number. The stability analysis of the flow past the airfoil is carried out under very small spanwise wavenumber β = 10−4 to approximate the two-dimensional perturbation, and medium and large spanwise wavenumbers (β = 1–8) to account for the three-dimensional perturbation. Numerical results reveal that under small spanwise wavenumber, there are at most two oscillatory unstable modes corresponding to the near wake and far wake instabilities; the growth rate and frequency of the perturbation agree well with the two-dimensional direct numerical simulation results under all Reynolds numbers. For a larger spanwise wavenumber β = 1, there is only one oscillatory unstable mode associated with the wake instability at Re = 400 and 600, while at Re = 800 and 1000 there are two oscillatory unstable modes for the near wake and far wake instabilities, and one stationary unstable mode for the monotonically growing perturbation within the recirculation bubble via the centrifugal instability mechanism. All the unstable modes are weakened or even suppressed as the spanwise wavenumber further increases, among which the stationary mode persists until β = 4.

  14. BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

    Zhang, Wei; Samtaney, Ravi

    2016-01-01

    We perform BiGlobal linear stability analysis on flow past a NACA0012 airfoil at 16° angle of attack and Reynolds number ranging from 400 to 1000. The steady-state two-dimensional base flows are computed using a well-tested finite difference code in combination with the selective frequency damping method. The base flow is characterized by two asymmetric recirculation bubbles downstream of the airfoil whose streamwise extent and the maximum reverse flow velocity increase with the Reynolds number. The stability analysis of the flow past the airfoil is carried out under very small spanwise wavenumber β = 10−4 to approximate the two-dimensional perturbation, and medium and large spanwise wavenumbers (β = 1–8) to account for the three-dimensional perturbation. Numerical results reveal that under small spanwise wavenumber, there are at most two oscillatory unstable modes corresponding to the near wake and far wake instabilities; the growth rate and frequency of the perturbation agree well with the two-dimensional direct numerical simulation results under all Reynolds numbers. For a larger spanwise wavenumber β = 1, there is only one oscillatory unstable mode associated with the wake instability at Re = 400 and 600, while at Re = 800 and 1000 there are two oscillatory unstable modes for the near wake and far wake instabilities, and one stationary unstable mode for the monotonically growing perturbation within the recirculation bubble via the centrifugal instability mechanism. All the unstable modes are weakened or even suppressed as the spanwise wavenumber further increases, among which the stationary mode persists until β = 4.

  15. Existence, stability, and dynamics of harmonically trapped one-dimensional multi-component solitary waves: The near-linear limit

    Xu, H.; Kevrekidis, P. G.; Kapitula, T.

    2017-06-01

    In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrödinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of Lyapunov-Schmidt reduction methods allows us to identify persistence criteria for the different families of solutions which we classify as (m, n), in accordance with the number of zeros in each component. Upon developing the existence theory, we turn to a stability analysis of the different configurations, using the Krein signature and the Hamiltonian-Krein index as topological tools identifying the number of potentially unstable eigendirections for each branch. A perturbation expansion for the eigenvalue problems associated with nonlinear states found near the linear limit permits us to obtain explicit asymptotic expressions for the eigenvalues. Finally, when the states are found to be unstable, typically by virtue of Hamiltonian Hopf bifurcations, their dynamics is studied in order to identify the nature of the respective instability. The dynamics is generally found to lead to a vibrational evolution over long time scales.

  16. Some Schrödinger-type inequalities for stabilization of discrete linear systems associated with the stationary Schrödinger operator

    Zongcai Jiang

    2016-10-01

    Full Text Available Abstract By applying some Schrödinger-type inequalities developed by Huang (Int. J. Math. 27(2:1650009, 2016, we are concerned with stabilization of discrete linear systems associated with the Schrödinger operator. Our first aim is to prove a state-dependent switching law associated with the Schrödinger operator, which is based on a convex combination. Next, we derive sufficient conditions associated with the Schrödinger operator that guarantee the uniform exponential stability of the system. Finally, we propose a necessary and sufficient condition for the stability of a system with two Schrödinger subsystems.

  17. Design of indirectly driven, high-compression Inertial Confinement Fusion implosions with improved hydrodynamic stability using a 4-shock adiabat-shaped drive

    Milovich, J. L., E-mail: milovich1@llnl.gov; Robey, H. F.; Clark, D. S.; Baker, K. L.; Casey, D. T.; Cerjan, C.; Field, J.; MacPhee, A. G.; Pak, A.; Patel, P. K.; Peterson, J. L.; Smalyuk, V. A.; Weber, C. R. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

    2015-12-15

    Experimental results from indirectly driven ignition implosions during the National Ignition Campaign (NIC) [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] achieved a record compression of the central deuterium-tritium fuel layer with measured areal densities up to 1.2 g/cm{sup 2}, but with significantly lower total neutron yields (between 1.5 × 10{sup 14} and 5.5 × 10{sup 14}) than predicted, approximately 10% of the 2D simulated yield. An order of magnitude improvement in the neutron yield was subsequently obtained in the “high-foot” experiments [O. A. Hurricane et al., Nature 506, 343 (2014)]. However, this yield was obtained at the expense of fuel compression due to deliberately higher fuel adiabat. In this paper, the design of an adiabat-shaped implosion is presented, in which the laser pulse is tailored to achieve similar resistance to ablation-front instability growth, but with a low fuel adiabat to achieve high compression. Comparison with measured performance shows a factor of 3–10× improvement in the neutron yield (>40% of predicted simulated yield) over similar NIC implosions, while maintaining a reasonable fuel compression of >1 g/cm{sup 2}. Extension of these designs to higher laser power and energy is discussed to further explore the trade-off between increased implosion velocity and the deleterious effects of hydrodynamic instabilities.

  18. The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

    Chang, Chau-Lyan

    2003-01-01

    During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary

  19. The investigation of the phase-locking stability in linear arrays of Josephson junctions and arrays closed into a superconducting loop

    Darula, M.; Seidel, P.; Misanik, B.; Busse, F.; Heinz, E.; Benacka, S.

    1994-01-01

    The phase-locking stability is investigated theoretically in two structures: linear arrays of Josephson junctions shunted by resistive load and arrays closed into superconducting loop. In both cases the quasi-identical junctions are supposed to be in arrays. The stability as a function of spread in Josephson junction parameters as well as a function of other circuit parameters is investigated. Using Floquet theory it is shown that spread in critical currents of Josephson junction limit the stability of phase-locking state. From the simulations it follows that the phase-locking in arrays closed into superconducting loop is more stable against the spread in junction parameters than in the case of linear array of Josephson junctions. (orig.)

  20. Elasto-hydrodynamic lubrication

    Dowson, D; Hopkins, D W

    1977-01-01

    Elasto-Hydrodynamic Lubrication deals with the mechanism of elasto-hydrodynamic lubrication, that is, the lubrication regime in operation over the small areas where machine components are in nominal point or line contact. The lubrication of rigid contacts is discussed, along with the effects of high pressure on the lubricant and bounding solids. The governing equations for the solution of elasto-hydrodynamic problems are presented.Comprised of 13 chapters, this volume begins with an overview of elasto-hydrodynamic lubrication and representation of contacts by cylinders, followed by a discussio

  1. Elementary classical hydrodynamics

    Chirgwin, B H; Langford, W J; Maxwell, E A; Plumpton, C

    1967-01-01

    Elementary Classical Hydrodynamics deals with the fundamental principles of elementary classical hydrodynamics, with emphasis on the mechanics of inviscid fluids. Topics covered by this book include direct use of the equations of hydrodynamics, potential flows, two-dimensional fluid motion, waves in liquids, and compressible flows. Some general theorems such as Bernoulli's equation are also considered. This book is comprised of six chapters and begins by introducing the reader to the fundamental principles of fluid hydrodynamics, with emphasis on ways of studying the motion of a fluid. Basic c

  2. Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

    Hu, Jun; Hadid, Hamda Ben; Henry, Daniel; Mojtabi, Abdelkader

    Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, ) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (0), and oscillatory for =0 remains so for >0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

  3. Analysis on Accuracy of Bias, Linearity and Stability of Measurement System in Ball screw Processes by Simulation

    Fan-Yun Pai

    2015-11-01

    Full Text Available To consistently produce high quality products, a quality management system, such as the ISO9001, 2000 or TS 16949 must be practically implemented. One core instrument of the TS16949 MSA (Measurement System Analysis is to rank the capability of a measurement system and ensure the quality characteristics of the product would likely be transformed through the whole manufacturing process. It is important to reduce the risk of Type I errors (acceptable goods are misjudged as defective parts and Type II errors (defective parts are misjudged as good parts. An ideal measuring system would have the statistical characteristic of zero error, but such a system could hardly exist. Hence, to maintain better control of the variance that might occur in the manufacturing process, MSA is necessary for better quality control. Ball screws, which are a key component in precision machines, have significant attributes with respect to positioning and transmitting. Failures of lead accuracy and axial-gap of a ball screw can cause negative and expensive effects in machine positioning accuracy. Consequently, a functional measurement system can incur great savings by detecting Type I and Type II errors. If the measurement system fails with respect to specification of the product, it will likely misjudge Type I and Type II errors. Inspectors normally follow the MSA regulations for accuracy measurement, but the choice of measuring system does not merely depend on some simple indices. In this paper, we examine the stability of a measuring system by using a Monte Carlo simulation to establish bias, linearity variance of the normal distribution, and the probability density function. Further, we forecast the possible area distribution in the real case. After the simulation, the measurement capability will be improved, which helps the user classify the measurement system and establish measurement regulations for better performance and monitoring of the precision of the ball screw.

  4. A model for the linear stability of the interface between aqueous humor and vitreous substitutes after vitreoretinal surgery

    Isakova, Krystyna; Pralits, Jan O.; Repetto, Rodolfo; Romano, Mario R.

    2014-12-01

    We consider the motion of two immiscible viscous fluids induced by periodic oscillations of a flat solid surface along its plane. The interface between the two fluids is parallel to the solid wall; one fluid occupies the region between the wall and the interface and the other extends from the interface to infinity. We study numerically the linear stability of the interface with respect to two-dimensional perturbations using the normal mode analysis and assuming quasi-steady flow conditions. The analysis is motivated by the need of understanding the behavior of vitreous substitutes inserted in the vitreous chamber of the eye after vitrectomy. This is a common surgical procedure adopted to treat retinal detachments, whereby the vitreous humor is removed from the eye and replaced by fluids immiscible with water. Owing to their hydrophobic nature, vitreous substitutes coexist in the vitreous chamber with a certain amount of aqueous humor (the fluid produced in the anterior part of the eye) and, typically, a thin layer of aqueous separates the tamponade fluid from the retina. A common problem with this treatment is that, in some cases, the interface between the two fluids breaks down and this might eventually lead to the generation of an emulsion. It is believed that mechanics plays an important role in this process but the problem remains very poorly understood. We find that instability of the interface is possible in a range of parameters that is relevant for the problem that motivated the present analysis. This suggests that shear instability is likely a possible mechanism triggering the onset of vitreous substitutes-aqueous interface instability.

  5. Propagation and stability characteristics of a 500-m-long laser-based fiducial line for high-precision alignment of long-distance linear accelerators.

    Suwada, Tsuyoshi; Satoh, Masanori; Telada, Souichi; Minoshima, Kaoru

    2013-09-01

    A laser-based alignment system with a He-Ne laser has been newly developed in order to precisely align accelerator units at the KEKB injector linac. The laser beam was first implemented as a 500-m-long fiducial straight line for alignment measurements. We experimentally investigated the propagation and stability characteristics of the laser beam passing through laser pipes in vacuum. The pointing stability at the last fiducial point was successfully obtained with the transverse displacements of ±40 μm level in one standard deviation by applying a feedback control. This pointing stability corresponds to an angle of ±0.08 μrad. This report contains a detailed description of the experimental investigation for the propagation and stability characteristics of the laser beam in the laser-based alignment system for long-distance linear accelerators.

  6. On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

    Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

    2017-04-01

    We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

  7. Black Hole Scrambling from Hydrodynamics.

    Grozdanov, Sašo; Schalm, Koenraad; Scopelliti, Vincenzo

    2018-06-08

    We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-N_{c} holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

  8. Medium-Term Stability of the Photon Beam Energy of An Elekta CompactTM Linear Accelerator Based on Daily Measurements of Beam Quality Factor

    Mohammad Amin Mosleh-Shirazi

    2016-04-01

    Full Text Available Introduction In this study, we aimed to assess the medium-term energy stability of a 6MV Elekta CompactTM linear accelerator. To the best of our knowledge, this is the first published article to evaluate this linear accelerator in terms of energy stability. As well as investigating the stability of the linear accelerator energy over a period of several weeks, the results will be useful for estimation of the required tolerance values for the beam quality factor (BQF of the PTW QUICKCHECK weblineTM (QCW daily checking device. Materials and Methods Over a 13 week period of routine clinical service, 52 daily readings of BQF were taken and then analyzed for a 10×10 cm2 field. Results No decreasing or increasing trend in BQF was observed over the study period. The mean BQF value was estimated at 5.4483 with a standard deviation (SD of 0.0459 (0.8%. The mean value was only 0.1% different from the baseline value. Conclusion The results of this medium-term stability study of the Elekta Compact linear accelerator energy showed that 96.2% of the observed BQF values were within ±1.3% of the baseline value. This can be considered to be within the recommended tolerance for linear accelerator photon beam energy. If an approach of applying ±3 SD is taken, the tolerance level for BQF may be suggested to be set at ±2.5%. However, further research is required to establish a relationship between BQF value and the actual changes in beam energy and penetrative quality.

  9. Laser driven hydrodynamic instability experiments

    Remington, B.A.; Weber, S.V.; Haan, S.W.; Kilkenny, J.D.; Glendinning, S.G.; Wallace, R.J.; Goldstein, W.H.; Wilson, B.G.; Nash, J.K.

    1992-01-01

    We have conducted an extensive series of experiments on the Nova laser to measure hydrodynamic instabilities in planar foils accelerated by x-ray ablation. Single mode experiments allow a measurement of the fundamental growth rates from the linear well into the nonlinear regime; multimode foils allow an assessment of the degree of mode coupling; and surface-finish experiments allow a measurement of the evolution of a broad spectrum of random initial modes. Experimental results and comparisons with theory and simulations are presented

  10. Electronic structure, stability and non-linear optical properties of aza-fullerenes C60-2nN2n(n=1–12

    K. Srinivasu

    2012-12-01

    Full Text Available Through ab initio based density functional theory calculations, we have investigated the electronic structure, stability and non-linear optical properties of a series of nitrogen substituted fullerenes (azafullerenes with the general formula C60-2nN2n (n=1–12. For each system, we have considered different possible isomers and the minimum energy isomer is subjected to further detailed investigations. We have calculated different properties such as HOMO-LUMO gaps, vertical ionization potentials, vertical electron affinities, etc. to verify the stability of the considered fullerenes. From the Hessian calculations, it is observed that all the fullerenes are not only associated with real vibrational frequencies, but the minimum frequencies are also found to be considerably large which further confirms the stability of the considered fullerenes. We find that the presence of unperturbed C6 rings enhances the stability of the fullerene whereas, the -N-C-N- fragments are found to destabilize the structure. At lower doping concentration, the stabilization due to C6 is more predominant and as the doping concentration is increased, the destabilization due to nitrogen-nitrogen repulsion plays a more important role. Our calculated polarizability and hyperpolarizability parameters of C60 are found to be in good agreement with the earlier reported results. On nitrogen doping, considerable variation is observed in the non-linear optical coefficients, which can be helpful in designing new photonic devices.

  11. On Some Sufficiency-Type Stability and Linear State-Feedback Stabilization Conditions for a Class of Multirate Discrete-Time Systems

    M. De la Sen

    2018-05-01

    Full Text Available This paper presents and discusses the stability of a discrete multirate sampling system whose sets of sampling rates (or sampling periods are the integer multiple of those operating on all the preceding substates. Each of such substates is associated with a particular sampling rate. The sufficiency-type stability conditions are derived based on simple conditions on the norm, spectral radius and numerical radius of the matrix of the dynamics of a system parameterized at the largest sampling period.

  12. A geometric criterion for the stability of forced oscillations in non-linear mechanics (1961); Un critere geometrique de stabilite des oscillations forcees en mecanique non lineaire (1961)

    Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1961-07-01

    The author completes the two-parameter diagram theory which he has previously explained, by giving a geometric criterion of stability for a non-linear system under forced conditions. After two simple geometric transformations of the diagram he obtains the separators which are the boundary conditions for the zones of stability. (author) [French] L'auteur complete la theorie du diagramme a deux parametres, qu'il a anterieurement exposee, par l'enonce d'un critere geometrique de stabilite, relatif aux regimes forces d'un systeme non lineaire. Il obtient, par deux transformations geometriques simples du diagramme, les separatrices qui delimitent les zones de stabilite. (auteur)

  13. Assortative mating and directional or stabilizing selection for a non-linear function of traits in Tribolium.

    Campo, J L; Gil, M G

    1993-01-12

    Assortative or random mating following selection in either direction on a non-linear index (experiment 1) or stabilizing selection for pupal length (experiment 2) were carried out for five generations in two lines of Tribolium castaneum (A and R, respectively), with three replicates each. The selected proportion was 25% in all lines. In experiment 1, the selection criterion was designed to increase the aggregate value of adult weight and the first- and second-order powers of pupal length. The A and R lines gave significant responses for the aggregate value (184 ± 6 and 161 ± 14, respectively), pupal length (0.74 ± 0.02 and 0.64 ± 0.05, respectively), and adult weight (0.79 ± 0.03 and 0.78 ± 0.12, respectively). Although the A line was not significantly better than the R line, there was a consistent advantage for assortative mating over random mating, the mean response for aggregate value and pupal length being approximately 1.15 times greater for the A line. In experiment 2 the selection criterion was the square of the deviation from the mean pupal length (stabilizing selection); both lines did not show any change for pupal length. The phenotypic variance showed a significant decrease in the A and R lines, due to a decrease in between-family variance. The assortatively and randomly mated lines were similar for these changes in phenotypic variation. RESUMEN: Aparemiento clasificado y selección direccional o estabilizante para una función no lineal en Tribolium. Dos líneas de Tribolium castaneum fueron seleccionadas direccionalmente para un índice no lineal (experimento 1) o estabilizantemente para longitud de pupa (experimento 2), apareando los animales seleccionados clasificadamente (A) o aleatoriamente (R). Había tres repeticiones por experimento y línea, siendo la proporción de selección el 25%. En el experimento 1, el objetivo de selección incluía el peso adulto así como la longitud de pupa y su cuadrado. Ambas líneas dieron respuesta

  14. Application of “Boomerang” Linear Polystyrene-Stabilized Pd Nanoparticles to a Series of C-C Coupling Reactions in Water

    Atsushi Ohtaka

    2015-02-01

    Full Text Available The application of a catch-and-release system for soluble Pd species between water (reaction medium and polystyrene (polymer support was examined in the Suzuki coupling reaction with 2-bromothiophene and the Heck reaction with styrene or bromobenzene. Although a slight increase in particle size was observed by TEM after re-stabilization of the Pd species on linear polystyrene, no agglomeration was observed.

  15. Numerical analysis of anisotropic diffusion effect on ICF hydrodynamic instabilities

    Olazabal-Loumé M.

    2013-11-01

    Full Text Available The effect of anisotropic diffusion on hydrodynamic instabilities in the context of Inertial Confinement Fusion (ICF flows is numerically assessed. This anisotropy occurs in indirect-drive when laminated ablators are used to modify the lateral transport [1,2]. In direct-drive, non-local transport mechanisms and magnetic fields may modify the lateral conduction [3]. In this work, numerical simulations obtained with the code PERLE [4], dedicated to linear stability analysis, are compared with previous theoretical results [5]. In these approaches, the diffusion anisotropy can be controlled by a characteristic coefficient which enables a comprehensive study. This work provides new results on the ablative Rayleigh-Taylor (RT, ablative Richtmyer-Meshkov (RM and Darrieus-Landau (DL instabilities.

  16. Stabilization

    Muhammad H. Al-Malack

    2016-07-01

    Full Text Available Fuel oil flyash (FFA produced in power and water desalination plants firing crude oils in the Kingdom of Saudi Arabia is being disposed in landfills, which increases the burden on the environment, therefore, FFA utilization must be encouraged. In the current research, the effect of adding FFA on the engineering properties of two indigenous soils, namely sand and marl, was investigated. FFA was added at concentrations of 5%, 10% and 15% to both soils with and without the addition of Portland cement. Mixtures of the stabilized soils were thoroughly evaluated using compaction, California Bearing Ratio (CBR, unconfined compressive strength (USC and durability tests. Results of these tests indicated that stabilized sand mixtures could not attain the ACI strength requirements. However, marl was found to satisfy the ACI strength requirement when only 5% of FFA was added together with 5% of cement. When the FFA was increased to 10% and 15%, the mixture’s strength was found to decrease to values below the ACI requirements. Results of the Toxicity Characteristics Leaching Procedure (TCLP, which was performed on samples that passed the ACI requirements, indicated that FFA must be cautiously used in soil stabilization.

  17. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel

    2015-01-01

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search

  18. Linear stability of a fuel channel uniformly heated considering retrofeeding by vacuum. Theoretical study; Estabilidad lineal de un canal combustible uniformemente calentado considerando retroalimentacion por vacios

    Gonzalez M, V. [Comision Nacional de Seguridad Nuclear y Salvaguardias, 03000 Mexico D.F. (Mexico); Salinas H, J.G.; Espinosa P, G. [Universidad Autonoma Metropolitana-Iztapalapa, 09000 Mexico D.F. (Mexico)

    2000-07-01

    The Technology, Regulation and Services Management of the National Commission of Nuclear Safety and Safeguards in coordinated form with the IPH Department of the Metropolitan Autonomous-Iztapalapa University, developed the present project to study the linear stability in a fuel channel uniformly heated with effects of retrofeeding by vacuums. In this study the methodology used in the analysis of linear stability of the nuclear reactor unit 1 at Laguna Verde power plant is described which represented by an average channel uniformly heated. The conceptual model consists of two cells which represent the two regions in which is divided the channel according to the cooling is in one and two phases, considering the boiling length dependent in the time. It is used the homogeneous flux models for describing the thermohydraulic behavior of the cooling in the two phases region. The neutron processes with the punctual model of the neutron kinetics with a group of retarded neutrons precursors are described. It is studied the behavior of the system in the frequency domain with the transfer functions obtained and it is characterized in four operation states corresponding to the four corners of the low stability zone in the map power-flow Laguna Verde power plant. For these operation states the characteristic frequency is determined and the corresponding Nyquist diagrams are obtained. The results show that the system stability depends on the power-flow relation and that the operations which implicate a reduction of this relation improve the stability of the system (reducing the power introducing control bars with constant cooling flow or increase cooling flow with bars pattern established). The obtained results with effects of retrofeeding by vacuums show that the value of the characteristic frequency is modified very little with respect to the model without retrofeeding, therefore the thermohydraulic processes seem to determine the response of the stability of the system

  19. The molar hydrodynamic volume changes of factor VIIa due to GlycoPEGylation

    Plesner, Bitten; Westh, Peter; Hvidt, Søren

    2011-01-01

    The effects of GlycoPEGylation on the molar hydrodynamic volume of recombinant human rFVIIa were investigated using rFVIIa and two GlycoPEGylated recombinant human FVIIa derivatives, a linear 10 kDa PEG and a branched 40 kDa PEG, respectively. Molar hydrodynamic volumes were determined by capillary......, that the molar hydrodynamic volume of the conjugated protein is not just an addition of the molar hydrodynamic volume of the PEG and the protein. The molar hydrodynamic volume of the GlycoPEGylated protein is larger than the volume of its composites. These results suggest that both the linear and the branched...

  20. An improved lattice hydrodynamic model considering the influence of optimal flux for forward looking sites

    Wang, Yunong; Ge, Hongxia; Cheng, Rongjun

    2017-11-01

    In this paper, a lattice hydrodynamic model is derived considering the delayed-feedback control influence of optimal flux for forward looking sites on a single-lane road which includes more comprehensive information. The control method is used to analyze the stability of the model. The critical condition for the linear steady traffic flow is deduced and the numerical simulation is carried out to investigate the advantage of the proposed model with and without the effect of optimal flux for forward looking sites. Moreover it indicates that the characteristic of the model can lead to a lower energy consumption in traffic system. The results are consistent with the theoretical analysis correspondingly.

  1. Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles.

    Lefauve, Adrien; Saintillan, David

    2014-02-01

    Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

  2. A lattice hydrodynamic model based on delayed feedback control considering the effect of flow rate difference

    Wang, Yunong; Cheng, Rongjun; Ge, Hongxia

    2017-08-01

    In this paper, a lattice hydrodynamic model is derived considering not only the effect of flow rate difference but also the delayed feedback control signal which including more comprehensive information. The control method is used to analyze the stability of the model. Furthermore, the critical condition for the linear steady traffic flow is deduced and the numerical simulation is carried out to investigate the advantage of the proposed model with and without the effect of flow rate difference and the control signal. The results are consistent with the theoretical analysis correspondingly.

  3. On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

    Valat, J.

    1960-12-01

    Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

  4. Mononuclear Clusterfullerene Single-Molecule Magnet Containing Strained Fused-Pentagons Stabilized by a Nearly Linear Metal Cyanide Cluster

    Liu, Fupin; Wang, Song; Gao, Cong Li

    2017-01-01

    Fused-pentagons results in an increase of local steric strain according to the isolated pentagon rule (IPR), and for all reported non-IPR clusterfullerenes multiple (two or three) metals are required to stabilize the strained fused-pentagons, making it difficult to access the single-atom properti...... (SMM)....

  5. Stabilization of the outputs of pulse amplifiers utilizing non-linear feedback networks. Application to nuclear spectrometer amplifiers

    Henein, K.L.

    1978-02-01

    In nuclear spectroscopy, baseline instability and random fluctuations at the output of the amplifier create imperfectly solved problems mainly at high counting rates. After a critical examination of current systems, solutions are proposed which surpass existing ones. It is shown that restorers and stabilizers of baselines have their own preferential application. Considering natural limits of performance the proposed solutions give entirely satisfactory results [fr

  6. Anisotropic hydrodynamics for conformal Gubser flow

    Strickland, Michael; Nopoush, Mohammad [Kent State University, Kent OH 44242 (United States); Ryblewski, Radoslaw [The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, PL-31342 Kraków (Poland)

    2016-12-15

    In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3){sub q} symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubser's ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.

  7. Anisotropic hydrodynamics for conformal Gubser flow

    Strickland, Michael; Nopoush, Mohammad; Ryblewski, Radoslaw

    2016-01-01

    In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3)_q symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubser's ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.

  8. Thermodynamic stabilities of linear and crinkled tapes and cyclic rosettes in melamine-cyanurate assemblies: a model description

    Bielejewska, A.G.; Marjo, Christopher E.; Prins, L.J.; Timmerman, P.; de Jong, Feike; Reinhoudt, David

    2001-01-01

    In this paper we describe model calculations for the self-assembly of N,N-disubstituted melamines 1 and N-substituted cyanuric acid or 5,5-disubstituted barbituric acid derivatives 2 into linear or crinkled tapes and cyclic rosettes via cooperative hydrogen bond formation. The model description

  9. Hydrodynamic optical soliton tunneling

    Sprenger, P.; Hoefer, M. A.; El, G. A.

    2018-03-01

    A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

  10. Fluctuating hydrodynamics for ionic liquids

    Lazaridis, Konstantinos [Department of Mathematics and Statistics, Washington State University, Pullman, 99163 (United States); Wickham, Logan [Department of Computer Science, Washington State University, Richland, 99354 (United States); Voulgarakis, Nikolaos, E-mail: n.voulgarakis@wsu.edu [Department of Mathematics and Statistics, Washington State University, Pullman, 99163 (United States)

    2017-04-25

    We present a mean-field fluctuating hydrodynamics (FHD) method for studying the structural and transport properties of ionic liquids in bulk and near electrified surfaces. The free energy of the system consists of two competing terms: (1) a Landau–Lifshitz functional that models the spontaneous separation of the ionic groups, and (2) the standard mean-field electrostatic interaction between the ions in the liquid. The numerical approach used to solve the resulting FHD-Poisson equations is very efficient and models thermal fluctuations with remarkable accuracy. Such density fluctuations are sufficiently strong to excite the experimentally observed spontaneous formation of liquid nano-domains. Statistical analysis of our simulations provides quantitative information about the properties of ionic liquids, such as the mixing quality, stability, and the size of the nano-domains. Our model, thus, can be adequately parameterized by directly comparing our prediction with experimental measurements and all-atom simulations. Conclusively, this work can serve as a practical mathematical tool for testing various theories and designing more efficient mixtures of ionic liquids. - Highlights: • A new fluctuating hydrodynamics method for ionic liquids. • Description of ionic liquid morphology in bulk and near electrified surfaces. • Direct comparison with experimental measurements.

  11. Analysis of linear stability in nuclear systems associated to two-phase fluid flow and in thermodynamic balance

    Galvao, O.B.; Amorim, E.S. do; D'Oliveira, A.B.

    1981-03-01

    Under special conditions a water-cooled reactor or other multiphase process can be subject to instabilities as the so called density-wave oscillations phenomenon. The purpose of this investigation is to derive the stability limits of a boiling channel for the dynamic response to an inlet velocity perturbation. The solution scheme allowed a coupling for the single and two-phase regions together with a model for the dynamic thermal response of the heated surface. The frequency response of a rational transfer function is obtained and a Nyquist plot is used for stability analysis. The model is, although simplified, quite capable of predicting the threshold for self-excited system or the trends given by more exact solution. (Author) [pt

  12. Investigation of cellular detonation structure formation via linear stability theory and 2D and 3D numerical simulations

    Borisov, S. P.; Kudryavtsev, A. N.

    2017-10-01

    Linear and nonlinear stages of the instability of a plane detonation wave (DW) and the subsequent process of formation of cellular detonation structure are investigated. A simple model with one-step irreversible chemical reaction is used. The linear analysis is employed to predict the DW front structure at the early stages of its formation. An emerging eigenvalue problem is solved with a global method using a Chebyshev pseudospectral method and the LAPACK software library. A local iterative shooting procedure is used for eigenvalue refinement. Numerical simulations of a propagation of a DW in plane and rectangular channels are performed with a shock capturing WENO scheme of 5th order. A special method of a computational domain shift is implemented in order to maintain the DW in the domain. It is shown that the linear analysis gives certain predictions about the DW structure that are in agreement with the numerical simulations of early stages of DW propagation. However, at later stages, a merger of detonation cells occurs so that their number is approximately halved. Computations of DW propagation in a square channel reveal two different types of spatial structure of the DW front, "rectangular" and "diagonal" types. A spontaneous transition from the rectangular to diagonal type of structure is observed during propagation of the DW.

  13. Theoretical and simulation research of hydrodynamic instabilities in inertial-confinement fusion implosions

    Wang, LiFeng; Ye, WenHua; He, XianTu; Wu, JunFeng; Fan, ZhengFeng; Xue, Chuang; Guo, HongYu; Miao, WenYong; Yuan, YongTeng; Dong, JiaQin; Jia, Guo; Zhang, Jing; Li, YingJun; Liu, Jie; Wang, Min; Ding, YongKun; Zhang, WeiYan

    2017-05-01

    Inertial fusion energy (IFE) has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world's energy future. It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion (ICF) hot-spot ignition scheme. In this mini-review, we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade. In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF, we first decompose the problem into different stages according to the implosion physics processes. The decomposed essential physics pro- cesses that are associated with ICF implosions, such as Rayleigh-Taylor instability (RTI), Richtmyer-Meshkov instability (RMI), Kelvin-Helmholtz instability (KHI), convergent geometry effects, as well as perturbation feed-through are reviewed. Analyti- cal models in planar, cylindrical, and spherical geometries have been established to study different physical aspects, including density-gradient, interface-coupling, geometry, and convergent effects. The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations. The KHI considering the ablation effect has been discussed in detail for the first time. A series of single-mode ablative RTI experiments has been performed on the Shenguang-II laser facility. The theoretical and simulation research provides us the physical insights of linear and weakly nonlinear growths, and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions, which has directly supported the research of ICF ignition target design. The ICF hot-spot ignition implosion design that uses several controlling features, based on our current understanding of hydrodynamic instabilities, to address shell implosion stability, has

  14. Stability investigations of relaxing molecular gas flows. Results and perspectives

    Grigor'ev, Yurii N.; Ershov, Igor V.

    2017-10-01

    This article presents results of systematic investigations of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The effect can be a new way for control stability and laminar turbulent transition in aerodynamic flows. The consideration of suppression of inviscid acoustic waves in 2D shear flows is presented. Nonlinear evolution of large-scale vortices and Kelvin — Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both classical linear and nonlinear energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of this article is to show the new dissipative effect, which can be used for flow control and laminarization.

  15. Small systems – hydrodynamics

    Bożek, Piotr, E-mail: piotr.bozek@fis.agh.edu.pl

    2016-12-15

    The scenario assuming a collective expansion stage in collisions of small systems, p-A, d-Au, and {sup 3}He-Au is discussed. A review of the observables predicted in relativistic hydrodynamic models in comparison with experimental data is presented, with arguments indicating the presence of collective expansion. The limits of applicability of the hydrodynamic model are addressed. We briefly indicate possible applications of the collective flow in small systems to study the space-time dynamics at very small scales in relativistic collisions.

  16. Desenvolvimento de um modelo numérico hidrodinâmico tri-dimensional linear, para a simulação e a previsão da circulação na plataforma brasileira, entre 23ºe 26ºS A three-dimensional linear hydrodynamical numerical model for the simulation and forecasting of circulation on the Brazilian shelf between 23º - 26º S

    Joseph Harari

    1985-01-01

    Full Text Available A three-dimensional linear hydrodynamical numerical model, Heaps type, was developed and applied to the southeastern Brazilian continental shelf, to simulate motions in the sea due to astronomical and meteorological effects. The first experiment of the model reproduced the propagation of the principal lunar tidal component (M2, allowing the plotting of its cotidal lines and current ellipses. In the second experiment, the circulation generated by astronomical factors only was simulated. And in the third experiment, the effect of the principal astronomical tidal components and meteorological effects observed in the area were reproduced, representing the total circulation in the shelf, in a period of high tidal elevations in the coast, due to the incursion of a deep cold front in this region.

  17. Hydrodynamical description of collective flow

    Huovinen, Pasi

    2003-01-01

    I review how hydrodynamical flow is related to the observed flow in ultrarelativistic heavy ion collisions and how initial conditions, equation of state and freeze-out temperature affect flow in hydrodynamical models.

  18. Dissipative relativistic hydrodynamics

    Imshennik, V.S.; Morozov, Yu.I.

    1989-01-01

    Using the comoving reference frame in the general non-inertial case, the relativistic hydrodynamics equations are derived with an account for dissipative effects in the matter. From the entropy production equation, the exact from for the dissipative tensor components is obtained. As a result, the closed system of equations of dissipative relativistic hydrodynamics is obtained in the comoving reference frame as a relativistic generalization of the known Navier-Stokes equations for Lagrange coordinates. Equations of relativistic hydrodynamics with account for dissipative effects in the matter are derived using the assocoated reference system in general non-inertial case. True form of the dissipative tensor components is obtained from entropy production equation. Closed system of equations for dissipative relativistic hydrodynamics is obtained as a result in the assocoated reference system (ARS) - relativistic generalization of well-known Navier-Stokes equations for Lagrange coordinates. Equation system, obtained in this paper for ARS, may be effectively used in numerical models of explosive processes with 10 51 erg energy releases which are characteristic for flashes of supernovae, if white dwarf type compact target suggested as presupernova

  19. Boltzmann equation and hydrodynamics beyond Navier-Stokes.

    Bobylev, A V

    2018-04-28

    We consider in this paper the problem of derivation and regularization of higher (in Knudsen number) equations of hydrodynamics. The author's approach based on successive changes of hydrodynamic variables is presented in more detail for the Burnett level. The complete theory is briefly discussed for the linearized Boltzmann equation. It is shown that the best results in this case can be obtained by using the 'diagonal' equations of hydrodynamics. Rigorous estimates of accuracy of the Navier-Stokes and Burnett approximations are also presented.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

  20. Connection between hydrodynamic, water bag and Vlasov models

    Gros, M.; Bertrand, P.; Feix, M.R.

    1978-01-01

    The connection between hydrodynamic, water bag and Vlasov models is still under consideration with numerical experiments. For long wavelength, slightly non linear excitations and initial preparations such as the usual adiabatic invariant Pn -3 is space independent, the hydrodynamic model is equivalent to the water bag, and for long wavelengths a nice agreement is found with the full numerical solution of the Vlasov equation. For other initial conditions when the water bag cannot be defined, the hydrodynamic approach does not represent the correct behaviour. (author)

  1. The stability of mechanical calibration for a kV cone beam computed tomography system integrated with linear accelerator

    Sharpe, Michael B.; Moseley, Douglas J.; Purdie, Thomas G.

    2006-01-01

    The geometric accuracy and precision of an image-guided treatment system were assessed. Image guidance is performed using an x-ray volume imaging (XVI) system integrated with a linear accelerator and treatment planning system. Using an amorphous silicon detector and x-ray tube, volumetric computed tomography images are reconstructed from kilovoltage radiographs by filtered backprojection. Image fusion and assessment of geometric targeting are supported by the treatment planning system. To assess the limiting accuracy and precision of image-guided treatment delivery, a rigid spherical target embedded in an opaque phantom was subjected to 21 treatment sessions over a three-month period. For each session, a volumetric data set was acquired and loaded directly into an active treatment planning session. Image fusion was used to ascertain the couch correction required to position the target at the prescribed iso-center. Corrections were validated independently using megavoltage electronic portal imaging to record the target position with respect to symmetric treatment beam apertures. An initial calibration cycle followed by repeated image-guidance sessions demonstrated the XVI system could be used to relocate an unambiguous object to within less than 1 mm of the prescribed location. Treatment could then proceed within the mechanical accuracy and precision of the delivery system. The calibration procedure maintained excellent spatial resolution and delivery precision over the duration of this study, while the linear accelerator was in routine clinical use. Based on these results, the mechanical accuracy and precision of the system are ideal for supporting high-precision localization and treatment of soft-tissue targets

  2. Microflow Cytometers with Integrated Hydrodynamic Focusing

    Martin Schmidt

    2013-04-01

    Full Text Available This study demonstrates the suitability of microfluidic structures for high throughput blood cell analysis. The microfluidic chips exploit fully integrated hydrodynamic focusing based on two different concepts: Two-stage cascade focusing and spin focusing (vortex principle. The sample—A suspension of micro particles or blood cells—is injected into a sheath fluid streaming at a substantially higher flow rate, which assures positioning of the particles in the center of the flow channel. Particle velocities of a few m/s are achieved as required for high throughput blood cell analysis. The stability of hydrodynamic particle positioning was evaluated by measuring the pulse heights distributions of fluorescence signals from calibration beads. Quantitative assessment based on coefficient of variation for the fluorescence intensity distributions resulted in a value of about 3% determined for the micro-device exploiting cascade hydrodynamic focusing. For the spin focusing approach similar values were achieved for sample flow rates being 1.5 times lower. Our results indicate that the performances of both variants of hydrodynamic focusing suit for blood cell differentiation and counting. The potential of the micro flow cytometer is demonstrated by detecting immunologically labeled CD3 positive and CD4 positive T-lymphocytes in blood.

  3. Hydrodynamic states of phonons in insulators

    S.A. Sokolovsky

    2012-12-01

    Full Text Available The Chapman-Enskog method is generalized for accounting the effect of kinetic modes on hydrodynamic evolution. Hydrodynamic states of phonon system of insulators have been studied in a small drift velocity approximation. For simplicity, the investigation was carried out for crystals of the cubic class symmetry. It has been found that in phonon hydrodynamics, local equilibrium is violated even in the approximation linear in velocity. This is due to the absence of phonon momentum conservation law that leads to a drift velocity relaxation. Phonon hydrodynamic equations which take dissipative processes into account have been obtained. The results were compared with the standard theory based on the local equilibrium validity. Integral equations have been obtained for calculating the objects of the theory (including viscosity and heat conductivity. It has been shown that in low temperature limit, these equations are solvable by iterations. Steady states of the system have been considered and an expression for steady state heat conductivity has been obtained. It coincides with the famous result by Akhiezer in the leading low temperature approximation. It has been established that temperature distribution in the steady state of insulator satisfies a condition of heat source absence.

  4. Hydrodynamics of Turning Flocks

    Yang, Xingbo; Marchetti, M. Cristina

    2014-01-01

    We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation o...

  5. A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

    Qin, Shunda; Ge, Hongxia; Cheng, Rongjun

    2018-02-01

    In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.

  6. Hydrodynamics of insect spermatozoa

    Pak, On Shun; Lauga, Eric

    2010-11-01

    Microorganism motility plays important roles in many biological processes including reproduction. Many microorganisms propel themselves by propagating traveling waves along their flagella. Depending on the species, propagation of planar waves (e.g. Ceratium) and helical waves (e.g. Trichomonas) were observed in eukaryotic flagellar motion, and hydrodynamic models for both were proposed in the past. However, the motility of insect spermatozoa remains largely unexplored. An interesting morphological feature of such cells, first observed in Tenebrio molitor and Bacillus rossius, is the double helical deformation pattern along the flagella, which is characterized by the presence of two superimposed helical flagellar waves (one with a large amplitude and low frequency, and the other with a small amplitude and high frequency). Here we present the first hydrodynamic investigation of the locomotion of insect spermatozoa. The swimming kinematics, trajectories and hydrodynamic efficiency of the swimmer are computed based on the prescribed double helical deformation pattern. We then compare our theoretical predictions with experimental measurements, and explore the dependence of the swimming performance on the geometric and dynamical parameters.

  7. Onset of Convection in the Presence of a Precipitation Reaction in a Porous Medium: A Comparison of Linear Stability and Numerical Approaches

    Parama Ghoshal

    2017-12-01

    Full Text Available Reactive convection in a porous medium has received recent interest in the context of the geological storage of carbon dioxide in saline formations. We study theoretically and numerically the gravitational instability of a diffusive boundary layer in the presence of a first-order precipitation reaction. We compare the predictions from normal mode, linear stability analysis, and nonlinear numerical simulations, and discuss the relative deviations. The application of our findings to the storage of carbon dioxide in a siliciclastic aquifer shows that while the reactive-diffusive layer can become unstable within a timescale of 1 to 1.5 months after the injection of carbon dioxide, it can take almost 10 months for sufficiently vigorous convection to produce a considerable increase in the dissolution flux of carbon dioxide.

  8. Emerging synthetic strategies for core cross-linked star (CCS) polymers and applications as interfacial stabilizers: bridging linear polymers and nanoparticles.

    Chen, Qijing; Cao, Xueteng; Xu, Yuanyuan; An, Zesheng

    2013-10-01

    Core cross-linked star (CCS) polymers become increasingly important in polymer science and are evaluated in many value-added applications. However, limitations exist to varied degrees for different synthetic methods. It is clear that improvement in synthetic efficiency is fundamental in driving this field moving even further. Here, the most recent advances are highlighted in synthetic strategies, including cross-linking with cross-linkers of low solubility, polymerization-induced self-assembly in aqueous-based heterogeneous media, and cross-linking via dynamic covalent bonds. The understanding of CCS polymers is also further refined to advocate their role as an intermediate between linear polymers and polymeric nanoparticles, and their use as interfacial stabilizers is rationalized within this context. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  9. Study on the estimation method of maneuvering hydrodynamic force in turning motion; Senkai undoji no soju ryutairyoku suiteiho ni kansuru kenkyu

    Kijima, K; Yukawa, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering; Maekawa, K [Hokkaido University, Sapporo (Japan). Faculty of Fisheries

    1996-04-10

    Estimation of the maneuvering performance of ships is very important from the viewpoint of safe navigation. Using three types of VLCCs (SR221A, B, C) with locally different stern frame lines as computational models, the estimation method of hull hydrodynamic force in turning motion was studied theoretically taking frame line shapes into account. The unstable behavior of courses was also studied using linear differential coefficients obtained from the estimation result on hull hydrodynamic force in oblique navigation and turning motion. As a result, the estimation result on hull hydrodynamic force was slightly different quantitatively from model test results in a range of large drift angle or turning angular velocity, while that was relatively well agreed with test results in a range of small such angle and velocity. As the study result on the unstable behavior of courses by using linear differential coefficients obtained from the estimation result on hull hydrodynamic force, determination of a course stability was possible by considering local difference in hull shape. 4 refs., 8 figs., 1 tab.

  10. Current linearity and operation stability in Al2O3-gate AlGaN/GaN MOS high electron mobility transistors

    Nishiguchi, Kenya; Kaneki, Syota; Ozaki, Shiro; Hashizume, Tamotsu

    2017-10-01

    To investigate current linearity and operation stability of metal-oxide-semiconductor (MOS) AlGaN/GaN high electron mobility transistors (HEMTs), we have fabricated and characterized the Al2O3-gate MOS-HEMTs without and with a bias annealing in air at 300 °C. Compared with the as-fabricated (unannealed) MOS HEMTs, the bias-annealed devices showed improved linearity of I D-V G curves even in the forward bias regime, resulting in increased maximum drain current. Lower subthreshold slope was also observed after bias annealing. From the precise capacitance-voltage analysis on a MOS diode fabricated on the AlGaN/GaN heterostructure, it was found that the bias annealing effectively reduced the state density at the Al2O3/AlGaN interface. This led to efficient modulation of the AlGaN surface potential close to the conduction band edge, resulting in good gate control of two-dimensional electron gas density even at forward bias. In addition, the bias-annealed MOS HEMT showed small threshold voltage shift after applying forward bias stress and stable operation even at high temperatures.

  11. Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system

    Jia, Zheng-Lin; Mei, Dong-Cheng

    2011-01-01

    We investigate numerically the effects of time delay on the phenomenon of noise-enhanced stability (NES) in a periodically modulated bistable system. Three types of time-delayed feedback, including linear delayed feedback, nonlinear delayed feedback and global delayed feedback, are considered. We find a non-monotonic behaviour of the mean first-passage time (MFPT) as a function of the delay time τ, with a maximum in the case of linear delayed feedback and with a minimum in the case of nonlinear delayed feedback. There are two peculiar values of τ around which the NES phenomenon is enhanced or weakened. For the case of global delayed feedback, the increase of τ always weakens the NES phenomenon. Moreover, we also show that the amplitude A and the frequency Ω of the periodic forcing play an opposite role in the NES phenomenon, i.e. the increase of A weakens the NES effect while the increase of Ω enhances it. These observations demonstrate that the time-delayed feedback can be used as a feasible control scheme for the NES phenomenon

  12. Transversal expansion study in the Landau hydrodynamic

    Pottag, F.W.

    1984-01-01

    The system of equations in the frame of Landau's hydrodynamical model for multiparticle production at high energies is studied. Taking as a first approximation the one-dimensional exact due to Khalatnikov, and a special set of curvilinear coordinates, the radial part is separated from the longitudinal one in the equations of motion, and a system of partial differential equations (non-linear, hyperbolic) is obtained for the radial part. These equations are solved numerically by the method of caracteristics. The hydrodynamical variables are obtained over all the three-dimensional-flow region as well as its variation with the mass of the initially expanding system. Both, the transverse rapidity distribution of the fluid and the inclusive particle distribution at 90 0 in the center of mass system, are calculated. The last one is compared with recent experimental data. (author) [pt

  13. Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

    Zhang, Wan-chao; Liu, Heng-xu; Zhang, Liang; Zhang, Xue-wei

    2016-12-01

    The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber's hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.

  14. Stability of parallel flows

    Betchov, R

    2012-01-01

    Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equation

  15. Titan's hydrodynamically escaping atmosphere

    Strobel, Darrell F.

    2008-02-01

    The upper atmosphere of Titan is currently losing mass at a rate ˜(4-5)×10 amus, by hydrodynamic escape as a high density, slow outward expansion driven principally by solar UV heating by CH 4 absorption. The hydrodynamic mass loss is essentially CH 4 and H 2 escape. Their combined escape rates are restricted by power limitations from attaining their limiting rates (and limiting fluxes). Hence they must exhibit gravitational diffusive separation in the upper atmosphere with increasing mixing ratios to eventually become major constituents in the exosphere. A theoretical model with solar EUV heating by N 2 absorption balanced by HCN rotational line cooling in the upper thermosphere yields densities and temperatures consistent with the Huygens Atmospheric Science Investigation (HASI) data [Fulchignoni, M., and 42 colleagues, 2005. Nature 438, 785-791], with a peak temperature of ˜185-190 K between 3500-3550 km. This model implies hydrodynamic escape rates of ˜2×10 CHs and 5×10 Hs, or some other combination with a higher H 2 escape flux, much closer to its limiting value, at the expense of a slightly lower CH 4 escape rate. Nonthermal escape processes are not required to account for the loss rates of CH 4 and H 2, inferred by the Cassini Ion Neutral Mass Spectrometer (INMS) measurements [Yelle, R.V., Borggren, N., de la Haye, V., Kasprzak, W.T., Niemann, H.B., Müller-Wodarg, I., Waite Jr., J.H., 2006. Icarus 182, 567-576].

  16. How to fake hydrodynamic signals

    Romatschke, Paul [Department of Physics, 390 UCB, University of Colorado at Boulder, Boulder, CO (United States); Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309 (United States)

    2016-12-15

    Flow signatures in experimental data from relativistic ion collisions, are usually interpreted as a fingerprint of the presence of a hydrodynamic phase during the evolution of these systems. I review some theoretical ideas to ‘fake’ this hydrodynamic behavior in p+A and A+A collisions. I find that transverse flow and femtoscopic measurements can easily be forged through non-hydrodynamic evolution, while large elliptic flow requires some non-vanishing interactions in the hot phase.

  17. Modeling hydrodynamic cavitation

    Kumar, P.S.; Pandit, A.B. [Mumbai Univ. (India). Chemical Engineering Div.

    1999-12-01

    Cavitation as a source and method of energy input for chemical processing is increasingly studied due to its ability to generate localized high temperatures and pressures under nearly ambient conditions. Compared to cavitation generated by ultrasound, hydrodynamic cavitation has been proved to be a very energy-efficient alternative. A simple and unified model has been developed to study the cavitation phenomena in hydraulic systems with emphasis on the venturi tube and high-speed homogenizer. The model has been found to be satisfactory in explaining the effect of operating variables and equipment geometry on two different modes of cavitation generation qualitatively and in some cases quantitatively. (orig.)

  18. Hydrodynamics of Ship Propellers

    Breslin, John P.; Andersen, Poul

    This book deals with flows over propellers operating behind ships, and the hydrodynamic forces and moments which the propeller generates on the shaft and on the ship hull.The first part of the text is devoted to fundamentals of the flow about hydrofoil sections (with and without cavitation...... of an intermittently cavitating propeller in a wake and the pressures and forces it exerts on the shaft and on the ship hull is examined. A final chapter discusses the optimization of efficiency of compound propulsors. The authors have taken care to clearly describe physical concepts and mathematical steps. Appendices...

  19. Foundations of radiation hydrodynamics

    Mihalas, Dimitri

    1999-01-01

    Radiation hydrodynamics is a broad subject that cuts across many disciplines in physics and astronomy: fluid dynamics, thermodynamics, statistical mechanics, kinetic theory, and radiative transfer, among others. The theory developed in this book by two specialists in the field can be applied to the study of such diverse astrophysical phenomena as stellar winds, supernova explosions, and the initial phases of cosmic expansion, as well as the physics of laser fusion and reentry vehicles. As such, it provides students with the basic tools for research on radiating flows.Largely self-contained,

  20. Nanoscale hydrodynamics near solids

    Camargo, Diego; de la Torre, J. A.; Duque-Zumajo, D.; Español, Pep; Delgado-Buscalioni, Rafael; Chejne, Farid

    2018-02-01

    Density Functional Theory (DFT) is a successful and well-established theory for the study of the structure of simple and complex fluids at equilibrium. The theory has been generalized to dynamical situations when the underlying dynamics is diffusive as in, for example, colloidal systems. However, there is no such a clear foundation for Dynamic DFT (DDFT) for the case of simple fluids in contact with solid walls. In this work, we derive DDFT for simple fluids by including not only the mass density field but also the momentum density field of the fluid. The standard projection operator method based on the Kawasaki-Gunton operator is used for deriving the equations for the average value of these fields. The solid is described as featureless under the assumption that all the internal degrees of freedom of the solid relax much faster than those of the fluid (solid elasticity is irrelevant). The fluid moves according to a set of non-local hydrodynamic equations that include explicitly the forces due to the solid. These forces are of two types, reversible forces emerging from the free energy density functional, and accounting for impenetrability of the solid, and irreversible forces that involve the velocity of both the fluid and the solid. These forces are localized in the vicinity of the solid surface. The resulting hydrodynamic equations should allow one to study dynamical regimes of simple fluids in contact with solid objects in isothermal situations.

  1. Anisotropic nonequilibrium hydrodynamic attractor

    Strickland, Michael; Noronha, Jorge; Denicol, Gabriel S.

    2018-02-01

    We determine the dynamical attractors associated with anisotropic hydrodynamics (aHydro) and the DNMR equations for a 0 +1 d conformal system using kinetic theory in the relaxation time approximation. We compare our results to the nonequilibrium attractor obtained from the exact solution of the 0 +1 d conformal Boltzmann equation, the Navier-Stokes theory, and the second-order Mueller-Israel-Stewart theory. We demonstrate that the aHydro attractor equation resums an infinite number of terms in the inverse Reynolds number. The resulting resummed aHydro attractor possesses a positive longitudinal-to-transverse pressure ratio and is virtually indistinguishable from the exact attractor. This suggests that an optimized hydrodynamic treatment of kinetic theory involves a resummation not only in gradients (Knudsen number) but also in the inverse Reynolds number. We also demonstrate that the DNMR result provides a better approximation of the exact kinetic theory attractor than the Mueller-Israel-Stewart theory. Finally, we introduce a new method for obtaining approximate aHydro equations which relies solely on an expansion in the inverse Reynolds number. We then carry this expansion out to the third order, and compare these third-order results to the exact kinetic theory solution.

  2. Load responsive hydrodynamic bearing

    Kalsi, Manmohan S.; Somogyi, Dezso; Dietle, Lannie L.

    2002-01-01

    A load responsive hydrodynamic bearing is provided in the form of a thrust bearing or journal bearing for supporting, guiding and lubricating a relatively rotatable member to minimize wear thereof responsive to relative rotation under severe load. In the space between spaced relatively rotatable members and in the presence of a liquid or grease lubricant, one or more continuous ring shaped integral generally circular bearing bodies each define at least one dynamic surface and a plurality of support regions. Each of the support regions defines a static surface which is oriented in generally opposed relation with the dynamic surface for contact with one of the relatively rotatable members. A plurality of flexing regions are defined by the generally circular body of the bearing and are integral with and located between adjacent support regions. Each of the flexing regions has a first beam-like element being connected by an integral flexible hinge with one of the support regions and a second beam-like element having an integral flexible hinge connection with an adjacent support region. A least one local weakening geometry of the flexing region is located intermediate the first and second beam-like elements. In response to application of load from one of the relatively rotatable elements to the bearing, the beam-like elements and the local weakening geometry become flexed, causing the dynamic surface to deform and establish a hydrodynamic geometry for wedging lubricant into the dynamic interface.

  3. Hydrodynamic instabilities in an ablation front

    Piriz, A R; Portugues, R F

    2004-01-01

    The hydrodynamic stability of an ablation front is studied for situations in which the wavelength of the perturbations is larger than the distance to the critical surface where the driving radiation is absorbed. An analytical model is presented, and it shows that under conditions in which the thermal flux is limited within the supercritical region of the ablative corona, the front may behave like a flame or like an ablation front, depending on the perturbation wavelength. For relatively long wavelengths the critical and ablation surfaces practically lump together into a unique surface and the front behaves like a flame, whereas for the shortest wavelengths the ablation front substructure is resolved

  4. Hydrodynamic instabilities in an ablation front

    Piriz, A R; Portugues, R F [E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)

    2004-06-01

    The hydrodynamic stability of an ablation front is studied for situations in which the wavelength of the perturbations is larger than the distance to the critical surface where the driving radiation is absorbed. An analytical model is presented, and it shows that under conditions in which the thermal flux is limited within the supercritical region of the ablative corona, the front may behave like a flame or like an ablation front, depending on the perturbation wavelength. For relatively long wavelengths the critical and ablation surfaces practically lump together into a unique surface and the front behaves like a flame, whereas for the shortest wavelengths the ablation front substructure is resolved.

  5. Hydrodynamic Forces on Composite Structures

    2014-06-01

    NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release; distribution is unlimited HYDRODYNAMIC ...Thesis 4. TITLE AND SUBTITLE HYDRODYNAMIC FORCES ON COMPOSITE STRUCTURES 5. FUNDING NUMBERS 6. AUTHOR(S) Scott C. Millhouse 7. PERFORMING...angles yields different free surface effects including vortices and the onset of cavitation . 14. SUBJECT TERMS Fluid structure interaction, FSI, finite

  6. Black brane entropy and hydrodynamics

    Booth, I.; Heller, M.P.; Spaliński, M.

    2010-01-01

    A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

  7. Black brane entropy and hydrodynamics

    Booth, I.; Heller, M.P.; Spaliński, M.

    2011-01-01

    A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics

  8. A hydrodynamic formalism for Brownian systems

    Pina, E.; Rosales, M.A.

    1981-01-01

    A formal hydrodynamic approach to Brownian motion is presented and the corresponding equations are derived. Hydrodynamic quantities are expressed in terms of the physical variables characterizing the Brownian systems. Contact is made with the hydrodynamic model of Quantum Mechanics. (author)

  9. Hydrodynamic processes in sharp meander bends and their morphological implications

    Blanckaert, K.

    2011-01-01

    The migration rate of sharp meander bends exhibits large variance and indicates that some sharply curved bends tend to stabilize. These observations remain unexplained. This paper examines three hydrodynamic processes in sharp bends with fixed banks and discusses their morphological implications:

  10. Hydrodynamic modelling of tidal inlets in Hue, Vietnam

    Lam, N.T.; Verhagen, H.J.; Van der Wegen, M.

    2003-01-01

    Application of an one-dimensional numerical model for hydrodynamic simulation of a complex lagooninlet system in Vietnam is presented. Model results help to get a better understanding on the behaviour of the system. Based on the numerical model results and analytic solutions, stability of tidal

  11. Foundations of radiation hydrodynamics

    Mihalas, D.; Mihalas, B. W.

    This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.

  12. From TDHF to hydrodynamics

    Koehler, H.S.

    1983-01-01

    The Time-Dependent Hartree-Fock theory provides a microscopic approach to the scattering of heavy ions. Fundamental in this theory is a mean-(one-body) field. The calculation of this field from a two-body effective interaction makes the theory microscopic. Many-body effects are included by the Brueckner definition of this interaction; the reaction-matrix. In excited media it is in general complex allowing for decays. The imaginary part relates directly to the collision-term in a transport equation. We treat this term by the time-relaxation-method. This implies an extension of the TDHF-equation to include two-body collisions. Hydrodynamic equations are derived from this new equation. The solution of the two equations agree quantitatively for short-relaxation-times. Relaxation-times are calculated as a function of temperature. (orig.)

  13. Hydrodynamics of Peristaltic Propulsion

    Athanassiadis, Athanasios; Hart, Douglas

    2014-11-01

    A curious class of animals called salps live in marine environments and self-propel by ejecting vortex rings much like jellyfish and squid. However, unlike other jetting creatures that siphon and eject water from one side of their body, salps produce vortex rings by pumping water through siphons on opposite ends of their hollow cylindrical bodies. In the simplest cases, it seems like some species of salp can successfully move by contracting just two siphons connected by an elastic body. When thought of as a chain of timed contractions, salp propulsion is reminiscent of peristaltic pumping applied to marine locomotion. Inspired by salps, we investigate the hydrodynamics of peristaltic propulsion, focusing on the scaling relationships that determine flow rate, thrust production, and energy usage in a model system. We discuss possible actuation methods for a model peristaltic vehicle, considering both the material and geometrical requirements for such a system.

  14. Hydrodynamic effects on coalescence.

    Dimiduk, Thomas G.; Bourdon, Christopher Jay; Grillet, Anne Mary; Baer, Thomas A.; de Boer, Maarten Pieter; Loewenberg, Michael (Yale University, New Haven, CT); Gorby, Allen D.; Brooks, Carlton, F.

    2006-10-01

    The goal of this project was to design, build and test novel diagnostics to probe the effect of hydrodynamic forces on coalescence dynamics. Our investigation focused on how a drop coalesces onto a flat surface which is analogous to two drops coalescing, but more amenable to precise experimental measurements. We designed and built a flow cell to create an axisymmetric compression flow which brings a drop onto a flat surface. A computer-controlled system manipulates the flow to steer the drop and maintain a symmetric flow. Particle image velocimetry was performed to confirm that the control system was delivering a well conditioned flow. To examine the dynamics of the coalescence, we implemented an interferometry capability to measure the drainage of the thin film between the drop and the surface during the coalescence process. A semi-automated analysis routine was developed which converts the dynamic interferogram series into drop shape evolution data.

  15. Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

    Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

    1992-01-01

    Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

  16. Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

    Font José A.

    2008-09-01

    Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable

  17. Frequency-dependent hydrodynamic interaction between two solid spheres

    Jung, Gerhard; Schmid, Friederike

    2017-12-01

    Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions between finite-sized particles in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that at high frequencies, the compressibility of the fluid has a significant impact on the frequency-dependent pair interactions. The predictions of hydrodynamic theory are compared to molecular dynamics simulations of two nanocolloids in a Lennard-Jones fluid. For this system, we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.

  18. Numerical analysis of hydrodynamic journal bearings lubricated with ferrofluid

    Montazeri, H.

    2008-01-01

    The current work focuses on studying the hydrodynamic characteristics of flow in journal bearings lubricated with ferrofluid. The bearing has an infinite length and operates under incompressible laminar flow and steady conditions. Assuming linear behaviour for the magnetic material of the

  19. Experimental Validation of a Wave Energy Converter Array Hydrodynamics Tool

    Ruiz, Pau Mercadé; Ferri, Francesco; Kofoed, Jens Peter

    2017-01-01

    This paper uses experimental data to validate a wave energy converter (WEC) array hydrodynamics tool developed within the context of linearized potential flow theory. To this end, wave forces and power absorption by an array of five-point absorber WECs in monochromatic and panchromatic waves were...

  20. Recent development of hydrodynamic modeling

    Hirano, Tetsufumi

    2014-09-01

    In this talk, I give an overview of recent development in hydrodynamic modeling of high-energy nuclear collisions. First, I briefly discuss about current situation of hydrodynamic modeling by showing results from the integrated dynamical approach in which Monte-Carlo calculation of initial conditions, quark-gluon fluid dynamics and hadronic cascading are combined. In particular, I focus on rescattering effects of strange hadrons on final observables. Next I highlight three topics in recent development in hydrodynamic modeling. These include (1) medium response to jet propagation in di-jet asymmetric events, (2) causal hydrodynamic fluctuation and its application to Bjorken expansion and (3) chiral magnetic wave from anomalous hydrodynamic simulations. (1) Recent CMS data suggest the existence of QGP response to propagation of jets. To investigate this phenomenon, we solve hydrodynamic equations with source term which exhibits deposition of energy and momentum from jets. We find a large number of low momentum particles are emitted at large angle from jet axis. This gives a novel interpretation of the CMS data. (2) It has been claimed that a matter created even in p-p/p-A collisions may behave like a fluid. However, fluctuation effects would be important in such a small system. We formulate relativistic fluctuating hydrodynamics and apply it to Bjorken expansion. We found the final multiplicity fluctuates around the mean value even if initial condition is fixed. This effect is relatively important in peripheral A-A collisions and p-p/p-A collisions. (3) Anomalous transport of the quark-gluon fluid is predicted when extremely high magnetic field is applied. We investigate this possibility by solving anomalous hydrodynamic equations. We found the difference of the elliptic flow parameter between positive and negative particles appears due to the chiral magnetic wave. Finally, I provide some personal perspective of hydrodynamic modeling of high energy nuclear collisions

  1. SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION

    Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)

    2016-12-20

    Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.

  2. Similarity flows in relativistic hydrodynamics

    Blaizot, J.P.; Ollitrault, J.Y.

    1986-01-01

    In ultra-relativistic heavy ion collisions, one expects in particular to observe a deconfinement transition leading to a formation of quark gluon plasma. In the framework of the hydrodynamic model, experimental signatures of such a plasma may be looked for as observable consequences of a first order transition on the evolution of the system. In most of the possible scenario, the phase transition is accompanied with discontinuities in the hydrodynamic flow, such as shock waves. The method presented in this paper has been developed to treat without too much numerical effort such discontinuous flow. It relies heavily on the use of similarity solutions of the hydrodynamic equations

  3. Chaotic hydrodynamics of fluidized beds

    Van der Stappen, M.L.M. [Unit Process and Systems Engineering, Advanced Manufacturing Technology Group, Unilever Research Laboratorium, Vlaardingen (Netherlands)

    1996-12-31

    The major goals of this thesis are: (1) to develop and evaluate an analysis method based on techniques from non-linear chaos theory to characterize the nonlinear hydrodynamics of gas-solids fluidized beds quantitatively; and (2) to determine the dependence of the chaotic invariants on the operating conditions and investigate how the chaos analysis method can be profitably applied to improve scale-up and design of gas-solids fluidized bed reactors. Chaos theory is introduced in chapter 2 with emphasis on analysis techniques for (experimental) time series, known from literature at the start of this work (1990-1991). In chapter 3, the testing of existing and newly developed techniques on both model and fluidized bed data is described. This leads to the development of the chaos analysis method to analyze measured pressure fluctuations time series of a fluidized bed. Following, in chapter 4, this method is tested and all choices for the parameters are evaluated. The influence of the experimental parameters and external disturbances on the measurements and analysis results is discussed and quantified. The result is a chaos measurement and analysis protocol, which is further used in this work. In chapter 5, the applications to fluidized beds are discussed. It is shown that the entropy is a good measure for the characterization of the dynamical behavior of gas-solids bubbling/slugging fluidized beds. Entropy is applied to characterize the influence of the operating conditions, to assess regime transitions and to analyze dimensionless similar beds of different scale. Quantitative design correlations that relate entropy to the operating parameters (including the bed diameter) are described. Finally, it is discussed how the results of this work might be used in scaling up the chaotic dynamics of fluidized beds. The overall conclusions and outlook from this work are presented in chapter 6. 182 refs.

  4. Lotic Water Hydrodynamic Model

    Judi, David Ryan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tasseff, Byron Alexander [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-01-23

    Water-related natural disasters, for example, floods and droughts, are among the most frequent and costly natural hazards, both socially and economically. Many of these floods are a result of excess rainfall collecting in streams and rivers, and subsequently overtopping banks and flowing overland into urban environments. Floods can cause physical damage to critical infrastructure and present health risks through the spread of waterborne diseases. Los Alamos National Laboratory (LANL) has developed Lotic, a state-of-the-art surface water hydrodynamic model, to simulate propagation of flood waves originating from a variety of events. Lotic is a two-dimensional (2D) flood model that has been used primarily for simulations in which overland water flows are characterized by movement in two dimensions, such as flood waves expected from rainfall-runoff events, storm surge, and tsunamis. In 2013, LANL developers enhanced Lotic through several development efforts. These developments included enhancements to the 2D simulation engine, including numerical formulation, computational efficiency developments, and visualization. Stakeholders can use simulation results to estimate infrastructure damage and cascading consequences within other sets of infrastructure, as well as to inform the development of flood mitigation strategies.

  5. Hydrodynamics of rotating superfluids

    Chandler, E.A.

    1981-01-01

    In this thesis, a coarse grained hydrodynamics is developed from the exact description of Tkachenko. To account for the dynamics of the vortex lattice, the macroscopic vortex displacement field is treated as an independent degree of freedom. The conserved energy is written in terms of the coarse-grained normal fluid, superfluid, and vortex velocities and includes an elastic energy associated with deformations of the vortex lattice. Equations of motion consistent with the conservation of energy, entropy and vorticity and containing mutual friction terms arising from microscopic interactions between normal fluid excitations and the vortex lines are derived. When the vortex velocity is eliminated from the damping terms, this system of equations becomes essentially that of BK with added elastic terms in the momentum stress tensor and energy current. The dispersion relation and damping of the first and second sound modes and the two transverse modes sustained by the system are investigated. It is shown that mutual friction mixes the transverse modes of the normal and superfluid components and damps the transverse mode associated with the relative velocity of these components, making this wave evanescent in the plane perpendicular to the rotation axis. The wave associated with transverse motion of the total mass current is a generalized Tkachenko mode, whose dispersion relation reduces to that derived by Tkachenko wave when the wavevector lies in this plane

  6. Advanced in Macrostatistical Hydrodynamics

    Graham, A.L.; Tetlow, N.; Abbott, J.R.; Mondy, L.S.; Brenner, H.

    1993-01-01

    An overview is presented of research that focuses on slow flows of suspensions in which colloidal and inertial effects are negligibly small (Macrostatistical Hydrodynamics). First, we describe nuclear magnetic resonance imaging experiments to quantitatively measure particle migration occurring in concentrated suspensions undergoing a flow with a nonuniform shear rate. These experiments address the issue of how the flow field affects the microstructure of suspensions. In order to understand the local viscosity in a suspension with such a flow-induced, spatially varying concentration, one must know how the viscosity of a homogeneous suspension depends on such variables as solids concentration and particle orientation. We suggest the technique of falling ball viscometry, using small balls, as a method to determine the effective viscosity of a suspension without affecting the original microstructure significantly. We also describe data from experiments in which the detailed fluctuations of a falling ball's velocity indicate the noncontinuum nature of the suspension and may lead to more insights into the effects of suspension microstructure on macroscopic properties. Finally, we briefly describe other experiments that can be performed in quiescent suspensions (in contrast to the use of conventional shear rotational viscometers) in order to learn more about the microstructure and boundary effects in concentrated suspensions

  7. Engineering Hydrodynamic AUV Hulls

    Allen, J.

    2016-12-01

    AUV stands for autonomous underwater vehicle. AUVs are used in oceanography and are similar to gliders. MBARIs AUVs as well as other AUVs map the ocean floor which is very important. They also measure physical characteristics of the water, such as temperature and salinity. My science fair project for 4th grade was a STEM activity in which I built and tested 3 different AUV bodies. I wanted to find out which design was the most hydrodynamic. I tested three different lengths of AUV hulls to see which AUV would glide the farthest. The first was 6 inches. The second was 12 inches and the third was 18 inches. I used clay for the nosecone and cut a ruler into two and made it the fin. Each AUV used the same nosecone and fin. I tested all three designs in a pool. I used biomimicry to create my hypothesis. When I was researching I found that long slim animals swim fastest. So, my hypothesis is the longer AUV will glide farthest. In the end I was right. The longer AUV did glide the farthest.

  8. Hydrodynamics of electrons in graphene

    Lucas, Andrew; Chung Fong, Kin

    2018-02-01

    Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the ‘phase diagram’ of graphene, and the inevitable presence of impurities and phonons in experimental systems. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.

  9. Analytic approaches to relativistic hydrodynamics

    Hatta, Yoshitaka

    2016-12-15

    I summarize our recent work towards finding and utilizing analytic solutions of relativistic hydrodynamic. In the first part I discuss various exact solutions of the second-order conformal hydrodynamics. In the second part I compute flow harmonics v{sub n} analytically using the anisotropically deformed Gubser flow and discuss its dependence on n, p{sub T}, viscosity, the chemical potential and the charge.

  10. Hydrodynamic aspects of flotation separation

    Peleka Efrosyni N.

    2016-01-01

    Full Text Available Flotation separation is mainly used for removing particulates from aqueous dispersions. It is widely used for ore beneficiation and recovering valuable materials. This paper reviews the hydrodynamics of flotation separations and comments on selected recent publications. Units are distinguished as cells of ideal and non-ideal flow. A brief introduction to hydrodynamics is included to explain an original study of the hybrid flotation-microfiltration cell, effective for heavy metal ion removal.

  11. An introduction to astrophysical hydrodynamics

    Shore, Steven N

    1992-01-01

    This book is an introduction to astrophysical hydrodynamics for both astronomy and physics students. It provides a comprehensive and unified view of the general problems associated with fluids in a cosmic context, with a discussion of fluid dynamics and plasma physics. It is the only book on hydrodynamics that addresses the astrophysical context. Researchers and students will find this work to be an exceptional reference. Contents include chapters on irrotational and rotational flows, turbulence, magnetohydrodynamics, and instabilities.

  12. Hydrodynamic modeling of tsunamis from the Currituck landslide

    Geist, E.L.; Lynett, P.J.; Chaytor, J.D.

    2009-01-01

    Tsunami generation from the Currituck landslide offshore North Carolina and propagation of waves toward the U.S. coastline are modeled based on recent geotechnical analysis of slide movement. A long and intermediate wave modeling package (COULWAVE) based on the non-linear Boussinesq equations are used to simulate the tsunami. This model includes procedures to incorporate bottom friction, wave breaking, and overland flow during runup. Potential tsunamis generated from the Currituck landslide are analyzed using four approaches: (1) tsunami wave history is calculated from several different scenarios indicated by geotechnical stability and mobility analyses; (2) a sensitivity analysis is conducted to determine the effects of both landslide failure duration during generation and bottom friction along the continental shelf during propagation; (3) wave history is calculated over a regional area to determine the propagation of energy oblique to the slide axis; and (4) a high-resolution 1D model is developed to accurately model wave breaking and the combined influence of nonlinearity and dispersion during nearshore propagation and runup. The primary source parameter that affects tsunami severity for this case study is landslide volume, with failure duration having a secondary influence. Bottom friction during propagation across the continental shelf has a strong influence on the attenuation of the tsunami during propagation. The high-resolution 1D model also indicates that the tsunami undergoes nonlinear fission prior to wave breaking, generating independent, short-period waves. Wave breaking occurs approximately 40-50??km offshore where a tsunami bore is formed that persists during runup. These analyses illustrate the complex nature of landslide tsunamis, necessitating the use of detailed landslide stability/mobility models and higher-order hydrodynamic models to determine their hazard.

  13. Neutrino dark energy. Revisiting the stability issue

    Eggers Bjaelde, O.; Hannestad, S. [Aarhus Univ. (Denmark). Dept. of Physics and Astronomy; Brookfield, A.W. [Sheffield Univ. (United Kingdom). Dept. of Applied Mathematics and Dept. of Physics, Astro-Particle Theory and Cosmology Group; Van de Bruck, C. [Sheffield Univ. (United Kingdom). Dept. of Applied Mathematics, Astro-Particle Theory and Cosmology Group; Mota, D.F. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik]|[Institute of Theoretical Astrophysics, Oslo (Norway); Schrempp, L. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Tocchini-Valentini, D. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy

    2007-05-15

    A coupling between a light scalar field and neutrinos has been widely discussed as a mechanism for linking (time varying) neutrino masses and the present energy density and equation of state of dark energy. However, it has been pointed out that the viability of this scenario in the non-relativistic neutrino regime is threatened by the strong growth of hydrodynamic perturbations associated with a negative adiabatic sound speed squared. In this paper we revisit the stability issue in the framework of linear perturbation theory in a model independent way. The criterion for the stability of a model is translated into a constraint on the scalar-neutrino coupling, which depends on the ratio of the energy densities in neutrinos and cold dark matter. We illustrate our results by providing meaningful examples both for stable and unstable models. (orig.)

  14. Stability of cosmological detonation fronts

    Mégevand, Ariel; Membiela, Federico Agustín

    2014-05-01

    The steady-state propagation of a phase-transition front is classified, according to hydrodynamics, as a deflagration or a detonation, depending on its velocity with respect to the fluid. These propagation modes are further divided into three types, namely, weak, Jouguet, and strong solutions, according to their disturbance of the fluid. However, some of these hydrodynamic modes will not be realized in a phase transition. One particular cause is the presence of instabilities. In this work we study the linear stability of weak detonations, which are generally believed to be stable. After discussing in detail the weak detonation solution, we consider small perturbations of the interface and the fluid configuration. When the balance between the driving and friction forces is taken into account, it turns out that there are actually two different kinds of weak detonations, which behave very differently as functions of the parameters. We show that the branch of stronger weak detonations are unstable, except very close to the Jouguet point, where our approach breaks down.

  15. CALIBRATED HYDRODYNAMIC MODEL

    Sezar Gülbaz

    2015-01-01

    Full Text Available The land development and increase in urbanization in a watershed affect water quantityand water quality. On one hand, urbanization provokes the adjustment of geomorphicstructure of the streams, ultimately raises peak flow rate which causes flood; on theother hand, it diminishes water quality which results in an increase in Total SuspendedSolid (TSS. Consequently, sediment accumulation in downstream of urban areas isobserved which is not preferred for longer life of dams. In order to overcome thesediment accumulation problem in dams, the amount of TSS in streams and inwatersheds should be taken under control. Low Impact Development (LID is a BestManagement Practice (BMP which may be used for this purpose. It is a land planningand engineering design method which is applied in managing storm water runoff inorder to reduce flooding as well as simultaneously improve water quality. LID includestechniques to predict suspended solid loads in surface runoff generated over imperviousurban surfaces. In this study, the impact of LID-BMPs on surface runoff and TSS isinvestigated by employing a calibrated hydrodynamic model for Sazlidere Watershedwhich is located in Istanbul, Turkey. For this purpose, a calibrated hydrodynamicmodel was developed by using Environmental Protection Agency Storm WaterManagement Model (EPA SWMM. For model calibration and validation, we set up arain gauge and a flow meter into the field and obtain rainfall and flow rate data. Andthen, we select several LID types such as retention basins, vegetative swales andpermeable pavement and we obtain their influence on peak flow rate and pollutantbuildup and washoff for TSS. Consequently, we observe the possible effects ofLID on surface runoff and TSS in Sazlidere Watershed.

  16. Hydrodynamic escape from planetary atmospheres

    Tian, Feng

    Hydrodynamic escape is an important process in the formation and evolution of planetary atmospheres. Due to the existence of a singularity point near the transonic point, it is difficult to find transonic steady state solutions by solving the time-independent hydrodynamic equations. In addition to that, most previous works assume that all energy driving the escape flow is deposited in one narrow layer. This assumption not only results in less accurate solutions to the hydrodynamic escape problem, but also makes it difficult to include other chemical and physical processes in the hydrodynamic escape models. In this work, a numerical model describing the transonic hydrodynamic escape from planetary atmospheres is developed. A robust solution technique is used to solve the time dependent hydrodynamic equations. The method has been validated in an isothermal atmosphere where an analytical solution is available. The hydrodynamic model is applied to 3 cases: hydrogen escape from small orbit extrasolar planets, hydrogen escape from a hydrogen rich early Earth's atmosphere, and nitrogen/methane escape from Pluto's atmosphere. Results of simulations on extrasolar planets are in good agreement with the observations of the transiting extrasolar planet HD209458b. Hydrodynamic escape of hydrogen from other hypothetical close-in extrasolar planets are simulated and the influence of hydrogen escape on the long-term evolution of these extrasolar planets are discussed. Simulations on early Earth suggest that hydrodynamic escape of hydrogen from a hydrogen rich early Earth's atmosphere is about two orders magnitude slower than the diffusion limited escape rate. A hydrogen rich early Earth's atmosphere could have been maintained by the balance between the hydrogen escape and the supply of hydrogen into the atmosphere by volcanic outgassing. Origin of life may have occurred in the organic soup ocean created by the efficient formation of prebiotic molecules in the hydrogen rich early

  17. Matter suppression of collective SN neutrino oscillations and stability analysis

    Saviano, N.; Chakraborty, S.; Mirizzi, A.

    2014-01-01

    We perform a detailed analysis of the supernova (SN) neutrino flavor evolution during the early time accretion phase (post-bounce time t pb ≤ 500 ms), characterizing the ν signal by recent SN hydrodynamics simulations. We find that collective oscillations induced the ν-ν interactions in the deepest SN regions are suppressed by trajectory-dependent 'multi-angle' effects associated with the dense ordinary matter. We confirm this result with a linearized stability analysis of the neutrino equations of motion in presence of realistic neutrino energy with angle distributions. (authors)

  18. Study of vibrations and stabilization of linear collider final doublets at the sub-nanometer scale; Etude des vibrations et de la stabilisation a l'echelle sous-nanometrique des doublets finaux d'un collisionneur lineaire

    Bolzon, B

    2007-11-15

    CLIC is one of the current projects of high energy linear colliders. Vertical beam sizes of 0.7 nm at the time of the collision and fast ground motion of a few nanometers impose an active stabilization of the final doublets at a fifth of nanometer above 4 Hz. The majority of my work concerned vibrations and active stabilization study of cantilever and slim beams in order to be representative of the final doublets of CLIC. In a first part, measured performances of different types of vibration sensors associated to an appropriate instrumentation showed that accurate measurements of ground motion are possible from 0.1 Hz up to 2000 Hz on a quiet site. Also, electrochemical sensors answering a priori the specifications of CLIC can be incorporated in the active stabilization at a fifth of nanometer. In a second part, an experimental and numerical study of beam vibrations enabled to validate the efficiency of the numerical prediction incorporated then in the simulation of the active stabilization. Also, a study of the impact of ground motion and of acoustic noise on beam vibrations showed that an active stabilization is necessary at least up to 1000 Hz. In a third part, results on the active stabilization of a beam at its two first resonances are shown down to amplitudes of a tenth of nanometer above 4 Hz by using in parallel a commercial system performing passive and active stabilization of the clamping. The last part is related to a study of a support for the final doublets of a linear collider prototype in phase of finalization, the ATF2 prototype. This work showed that relative motion between this support and the ground is below imposed tolerances (6 nm above 0.1 Hz) with appropriate boundary conditions. (author)

  19. Soliton Gases and Generalized Hydrodynamics

    Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

    2018-01-01

    We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

  20. Anomalous hydrodynamics of Weyl materials

    Monteiro, Gustavo; Abanov, Alexander

    Kinetic theory is a useful tool to study transport in Weyl materials when the band-touching points are hidden inside a Fermi surface. It accounts, for example, for the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations (SdH effect) in the magnetoresistance together within the same framework. As an alternative approach to kinetic theory we also consider the regime of strong interactions where hydrodynamics can be applicable. A variational principle of these hydrodynamic equations can be found in and provide a natural framework to study hydrodynamic surface modes which correspond to the strongly-interacting physics signature of Fermi arcs. G.M. acknowledges the financial support from FAPESP.

  1. Brownian dynamics with hydrodynamic interactions

    Ermak, D.L.; McCammon, J.A.

    1978-01-01

    A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker--Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution

  2. Hydrodynamic instabilities in beryllium targets for the National Ignition Facility

    Yi, S. A., E-mail: austinyi@lanl.gov; Simakov, A. N.; Wilson, D. C.; Olson, R. E.; Kline, J. L.; Batha, S. H. [Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545 (United States); Clark, D. S.; Hammel, B. A.; Milovich, J. L.; Salmonson, J. D.; Kozioziemski, B. J. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94551 (United States)

    2014-09-15

    Beryllium ablators offer higher ablation velocity, rate, and pressure than their carbon-based counterparts, with the potential to increase the probability of achieving ignition at the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. We present here a detailed hydrodynamic stability analysis of low (NIF Revision 6.1) and high adiabat NIF beryllium target designs. Our targets are optimized to fully utilize the advantages of beryllium in order to suppress the growth of hydrodynamic instabilities. This results in an implosion that resists breakup of the capsule, and simultaneously minimizes the amount of ablator material mixed into the fuel. We quantify the improvement in stability of beryllium targets relative to plastic ones, and show that a low adiabat beryllium capsule can be at least as stable at the ablation front as a high adiabat plastic target.

  3. Stabilizing the thermal lattice Boltzmann method by spatial filtering.

    Gillissen, J J J

    2016-10-01

    We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.

  4. Abnormal pressures as hydrodynamic phenomena

    Neuzil, C.E.

    1995-01-01

    So-called abnormal pressures, subsurface fluid pressures significantly higher or lower than hydrostatic, have excited speculation about their origin since subsurface exploration first encountered them. Two distinct conceptual models for abnormal pressures have gained currency among earth scientists. The static model sees abnormal pressures generally as relict features preserved by a virtual absence of fluid flow over geologic time. The hydrodynamic model instead envisions abnormal pressures as phenomena in which flow usually plays an important role. This paper develops the theoretical framework for abnormal pressures as hydrodynamic phenomena, shows that it explains the manifold occurrences of abnormal pressures, and examines the implications of this approach. -from Author

  5. Anisotropic hydrodynamics: Motivation and methodology

    Strickland, Michael

    2014-06-15

    In this proceedings contribution I review recent progress in our understanding of the bulk dynamics of relativistic systems that possess potentially large local rest frame momentum-space anisotropies. In order to deal with these momentum-space anisotropies, a reorganization of relativistic viscous hydrodynamics can be made around an anisotropic background, and the resulting dynamical framework has been dubbed “anisotropic hydrodynamics”. I also discuss expectations for the degree of momentum-space anisotropy of the quark–gluon plasma generated in relativistic heavy ion collisions at RHIC and LHC from second-order viscous hydrodynamics, strong-coupling approaches, and weak-coupling approaches.

  6. Hydrodynamics of oceans and atmospheres

    Eckart, Carl

    1960-01-01

    Hydrodynamics of Oceans and Atmospheres is a systematic account of the hydrodynamics of oceans and atmospheres. Topics covered range from the thermodynamic functions of an ideal gas and the thermodynamic coefficients for water to steady motions, the isothermal atmosphere, the thermocline, and the thermosphere. Perturbation equations, field equations, residual equations, and a general theory of rays are also presented. This book is comprised of 17 chapters and begins with an introduction to the basic equations and their solutions, with the aim of illustrating the laws of dynamics. The nonlinear

  7. Hydrodynamic constants from cosmic censorship

    Nakamura, Shin

    2008-01-01

    We study a gravity dual of Bjorken flow of N=4 SYM-theory plasma. We point out that the cosmic censorship hypothesis may explain why the regularity of the dual geometry constrains the hydrodynamic constants. We also investigate the apparent horizon of the dual geometry. We find that the dual geometry constructed on Fefferman-Graham (FG) coordinates is not appropriate for examination of the apparent horizon since the coordinates do not cover the trapped region. However, the preliminary analysis on FG coordinates suggests that the location of the apparent horizon is very sensitive to the hydrodynamic parameters. (author)

  8. Hydrodynamic simulation of elliptic flow

    Kolb, P F; Ruuskanen, P V; Heinz, Ulrich W

    1999-01-01

    We use a hydrodynamic model to study the space-time evolution transverse to the beam direction in ultrarelativistic heavy-ion collisions with nonzero impact parameters. We focus on the influence of early pressure on the development of radial and elliptic flow. We show that at high energies elliptic flow is generated only during the initial stages of the expansion while radial flow continues to grow until freeze-out. Quantitative comparisons with SPS data from semiperipheral Pb+Pb collisions suggest the applicability of hydrodynamical concepts already $\\approx$ 1 fm/c after impact.

  9. Formulating viscous hydrodynamics for large velocity gradients

    Pratt, Scott

    2008-01-01

    Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor τ ij as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements τ ij . By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of τ ij . Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves. Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time

  10. Hydrodynamic instability of compressible fluid in porous medium

    Argal, Shraddha; Tiwari, Anita; Sharma, P K; Prajapati, R P

    2014-01-01

    The hydrodynamic Rayleigh -Taylor instability of two superposed compressible fluids in porous medium has been studied. The dispersion relation is derived for such a medium by using normal mode analysis. The RT instability is discussed for various simplified configuration. The effect of porosity and dynamic viscosity has been analyzed and it is observed that porosity and dynamic viscosity have stabilizing effect on the Rayleigh- Taylor instability of compressible fluids.

  11. Electrohydrodynamics and other hydrodynamic phenomena in continuous-flow electrophoresis

    Saville, D.A.

    1982-01-01

    The process known as continuous flow electrophoresis employs an electric field to separate the constituents of particulate samples suspended in a liquid. Complications arise because the electric field generates temperature gradients due to Joule heating and derives an electrohydrodynamic crossflow. Several aspects of the flow are discussed including entrance effects, hydrodynamic stability and a flow restructuring due to the combined effects of buoyancy and the crossflow. 10 references

  12. Nanoscale swimmers: hydrodynamic interactions and propulsion of molecular machines

    Sakaue, T.; Kapral, R.; Mikhailov, A. S.

    2010-06-01

    Molecular machines execute nearly regular cyclic conformational changes as a result of ligand binding and product release. This cyclic conformational dynamics is generally non-reciprocal so that under time reversal a different sequence of machine conformations is visited. Since such changes occur in a solvent, coupling to solvent hydrodynamic modes will generally result in self-propulsion of the molecular machine. These effects are investigated for a class of coarse grained models of protein machines consisting of a set of beads interacting through pair-wise additive potentials. Hydrodynamic effects are incorporated through a configuration-dependent mobility tensor, and expressions for the propulsion linear and angular velocities, as well as the stall force, are obtained. In the limit where conformational changes are small so that linear response theory is applicable, it is shown that propulsion is exponentially small; thus, propulsion is nonlinear phenomenon. The results are illustrated by computations on a simple model molecular machine.

  13. Plasmas in particle accelerators: a hydrodynamic model of three-dimensional electrostatic instabilities

    Krafft, G.A.; Mark, J.W.K.; Wang, T.S.F.

    1983-01-01

    In an earlier paper, closed hydrodynamic equations were derived with possible application to the simulation of beam plasmas relevant to designs of heavy ion accelerators for inertial confinement fusion energy applications. The closure equations involved a novel feature of anisotropic stresses even transverse to the beam. A related hydrodynamic model is used in this paper to examine further the boundaries of validity of such hydrodynamic approximations. It is also proposed as a useful tool to provide an economic means for searching the large parameter space relevant to three-dimensional stability problems involving coupling of longitudinal and transverse motions in the presence of wall impedance

  14. Generalized hydrodynamic transport in lattice-gas automata

    Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun

    1991-01-01

    The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

  15. Anomalous hydrodynamics in two dimensions

    Abstract. A new approach is presented to discuss two-dimensional hydrodynamics with gauge and gravitational anomalies. Exact constitutive relations for the stress tensor and charge current are obtained. Also, a connection between response parameters and anomaly coefficients is discussed. These are new results which, ...

  16. Topics in fluctuating nonlinear hydrodynamics

    Milner, S.T.

    1986-01-01

    Models of fluctuating nonlinear hydrodynamics have enjoyed much success in explaining the effect of long-wavelength fluctuations in diverse hydrodynamic systems. This thesis explores two such problems; in both, the body of hydrodynamic assumptions powerfully constrains the predictions of a well-posed theory. The effects of layer fluctuations in smectic-A liquid crystals are first examined. The static theory (introduced by Grinstein and Pelcovits) is reviewed. Ward identities, resulting from the arbitrariness of the layering direction, are derived and exploited. The static results motivate an examination of dynamic fluctuation effects. A new sound-damping experiment is proposed that would probe singular dependence of viscosities on applied stress. A theory of Procaccia and Gitterman that reaction rates of chemically reacting binary mixtures are drastically reduced near their thermodynamic critical points is analyzed. Hydrodynamic arguments and Van Hove theory are applied, concluding that the PG idea is drastically slowed, and spatially varying composition fluctuations are at best slowed down over a narrow range of wavenumbers

  17. Radiation hydrodynamics in the laboratory

    1985-12-01

    This report contains a collection of five preprints devoted to the subject of laser induced phenomena of radiation hydrodynamics. These preprints cover approximately the contents of the presentations made by the MPQ experimental laser-plasma group at the 17th European Conference on Laser Interaction with Matter (ECLIM), Rome, November 18-22, 1985. (orig.)

  18. Hydrodynamics of a quark droplet

    Bjerrum-Bohr, Johan J.; Mishustin, Igor N.; Døssing, Thomas

    2012-01-01

    We present a simple model of a multi-quark droplet evolution based on the hydrodynamical description. This model includes collective expansion of the droplet, effects of the vacuum pressure and surface tension. The hadron emission from the droplet is described following Weisskopf's statistical...

  19. Fish robotics and hydrodynamics

    Lauder, George

    2010-11-01

    Studying the fluid dynamics of locomotion in freely-swimming fishes is challenging due to difficulties in controlling fish behavior. To provide better control over fish-like propulsive systems we have constructed a variety of fish-like robotic test platforms that range from highly biomimetic models of fins, to simple physical models of body movements during aquatic locomotion. First, we have constructed a series of biorobotic models of fish pectoral fins with 5 fin rays that allow detailed study of fin motion, forces, and fluid dynamics associated with fin-based locomotion. We find that by tuning fin ray stiffness and the imposed motion program we can produce thrust both on the fin outstroke and instroke. Second, we are using a robotic flapping foil system to study the self-propulsion of flexible plastic foils of varying stiffness, length, and trailing edge shape as a means of investigating the fluid dynamic effect of simple changes in the properties of undulating bodies moving through water. We find unexpected non-linear stiffness-dependent effects of changing foil length on self-propelled speed, and as well as significant effects of trailing edge shape on foil swimming speed.

  20. Development of a numerical code for the analysis of the linear stability of the U1 and U2 reactors of the CNLV

    Espinosa P, G.; Estrada P, C.E.; Nunez C, A.; Amador G, R.

    2001-01-01

    The computer code ANESLI-1 developed by the CNSNS and UAM-I, has the main goal of making stability analysis of nuclear reactors of the BWR type, more specifically, the reactors of the U1 and U2 of the CNLV. However it can be used for another kind of applications. Its capacity of real time simulator, allows the prediction of operational transients, and conditions of dynamic steady states. ANESLI-1 was developed under a modular scheme, which allows to extend or/and to improve its scope. The lineal stability analysis predicts the instabilities produced by the wave density phenomenon. (Author)

  1. Linear Water Waves

    Kuznetsov, N.; Maz'ya, V.; Vainberg, B.

    2002-08-01

    This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

  2. Final Report. Hydrodynamics by high-energy-density plasma flow and hydrodynamics and radiative hydrodynamics with astrophysical application

    R Paul Drake

    2004-01-01

    OAK-B135 This is the final report from the project Hydrodynamics by High-Energy-Density Plasma Flow and Hydrodynamics and Radiation Hydrodynamics with Astrophysical Applications. This project supported a group at the University of Michigan in the invention, design, performance, and analysis of experiments using high-energy-density research facilities. The experiments explored compressible nonlinear hydrodynamics, in particular at decelerating interfaces, and the radiation hydrodynamics of strong shock waves. It has application to supernovae, astrophysical jets, shock-cloud interactions, and radiative shock waves

  3. A linear stability analysis of thermal convection in spherical shells with variable radial gravity based on the Tau-Chebyshev method

    Avila, Ruben; Cabello-González, Ares; Ramos, Eduardo

    2013-01-01

    Highlights: • The Tau-Chebyshev method solves the linear fluid flow equations in spherical shells. • The fluid motion is driven by a central force proportional to the radial position. • The full Navier–Stokes equations are solved by the spectral element method. • The linear results are verified with the solution of the Navier–Stokes equations. • The solution of the linear problems is used to initiate non-linear calculations. -- Abstract: The onset of thermal convection in a non-rotating spherical shell is investigated using linear theory. The Tau-Chebyshev spectral method is used to integrate the linearized equations. We investigate the onset of thermal convection by considering two cases of the radial gravitational field (i) a local acceleration, acting radially inward, that is proportional to the distance from the center r, and (ii) a radial gravitational central force that is proportional to r −n . The former case has been widely analyzed in the literature, because it constitutes a simplified model that is usually used, in astrophysics and geophysics, and is studied here to validate the numerical method. The latter case was analyzed since the case n = 5 has been experimentally realized (by means of the dielectrophoretic effect) under microgravity condition, in the experimental container called GeoFlow, inside the International Space Station. Our study is aimed to clarify the role of (i) a radially inward central force (either proportional to r or to r −n ), (ii) a base conductive temperature distribution provided by either a uniform heat source or an imposed temperature difference between outer and inner spheres, and (iii) the aspect ratio η (ratio of the radii of the inner and outer spheres), on the critical Rayleigh number. In all cases the surface of the spheres has been assumed to be rigid. The results obtained with the linear theory based on the Tau-Chebyshev spectral method are compared with those of the integration of the full non-linear

  4. Numerical Analysis of Combined Valve Hydrodynamic Characteristics for Turbine System

    Bhowmik, P. K.; Shamim, J. A.; Gairola, A.; Arif, M.; Suh, Kune Y. [Seoul National Univ., Seoul (Korea, Republic of)

    2014-05-15

    Flow characteristic curves are plotted by calculating the ratio of the measured mass flow rate versus the theoretical mass flow rate. The flow characteristic curves are utilized to accurately test the performance of the control valve of turbine system to ensure the highest controllability and reliability of the power conversion system of large and small power plants. Turbine converts the kinetic energy of steam to mechanical energy of rotor blades in power conversion system. The electrical energy output from the generator of which the rotor is coupled with that of the turbine depends on the rotation velocity of the turbine bucket. The rotation velocity is proportional to the mass flow rate (steam or gas) to the turbine through valves and nozzles. The turbine comprises fast acting governing control valves and stop valves acting against the seat in the flow passage in the closed position. The turbine control valve regulates the mass flow rate entering the first nozzle of a turbine. The main function of stop valve is to close the fluid inlet rapidly in response to a fast close signal to swiftly cut off the flow through the valve inlet. Both these valves contribute attractively to improvement of the power system transient stability as well. To improve the efficiency of power conversion system many investigation have been done by researcher by focusing on the cycle layout or working fluid or by improving the flow path of the working fluid. The main focus is to find out the best option for combined cycle power plant by analyzing four different cycle configuration. Next research phase focused on different way to enhance the cycle efficiency. As the electrical power output from the generator is proportional to the mass flow rate to the turbine through the valve, it should preferably operate linearly. In reality, however, the valve has the various flow characteristics pursuant to the stem lift. Thus, the flow characteristic and control performance are needed to be designed

  5. Numerical Analysis of Combined Valve Hydrodynamic Characteristics for Turbine System

    Bhowmik, P. K.; Shamim, J. A.; Gairola, A.; Arif, M.; Suh, Kune Y.

    2014-01-01

    Flow characteristic curves are plotted by calculating the ratio of the measured mass flow rate versus the theoretical mass flow rate. The flow characteristic curves are utilized to accurately test the performance of the control valve of turbine system to ensure the highest controllability and reliability of the power conversion system of large and small power plants. Turbine converts the kinetic energy of steam to mechanical energy of rotor blades in power conversion system. The electrical energy output from the generator of which the rotor is coupled with that of the turbine depends on the rotation velocity of the turbine bucket. The rotation velocity is proportional to the mass flow rate (steam or gas) to the turbine through valves and nozzles. The turbine comprises fast acting governing control valves and stop valves acting against the seat in the flow passage in the closed position. The turbine control valve regulates the mass flow rate entering the first nozzle of a turbine. The main function of stop valve is to close the fluid inlet rapidly in response to a fast close signal to swiftly cut off the flow through the valve inlet. Both these valves contribute attractively to improvement of the power system transient stability as well. To improve the efficiency of power conversion system many investigation have been done by researcher by focusing on the cycle layout or working fluid or by improving the flow path of the working fluid. The main focus is to find out the best option for combined cycle power plant by analyzing four different cycle configuration. Next research phase focused on different way to enhance the cycle efficiency. As the electrical power output from the generator is proportional to the mass flow rate to the turbine through the valve, it should preferably operate linearly. In reality, however, the valve has the various flow characteristics pursuant to the stem lift. Thus, the flow characteristic and control performance are needed to be designed

  6. Linear algebra

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  7. Hydrodynamics of vertical jumping in Archer fish

    Techet, Alexandra H.; Mendelson, Leah

    2017-11-01

    Vertical jumping for aerial prey from an aquatic environment requires both propulsive power and precise aim to succeed. Rapid acceleration to a ballistic velocity sufficient for reaching the prey height occurs before the fish leaves the water completely and experiences a thousandfold drop in force-producing ability. In addition to speed, accuracy and stability are crucial for successful feeding by jumping. This talk examines the physics of jumping using the archer fish as a model. Better known for their spitting abilities, archer fish will jump multiple body lengths out of the water for prey capture, from a stationary position just below the free surface. Modulation of oscillatory body kinematics and use of multiple fins for force production are identified as methods through which the fish can meet requirements for both acceleration and stabilization in limited space. Quantitative 3D PIV wake measurements reveal how variations in tail kinematics relate to thrust production throughout the course of a jumping maneuver and over a range of jump heights. By performing measurements in 3D, the timing, interactions, and relative contributions to thrust and lateral forces from each fin can be evaluated, elucidating the complex hydrodynamics that enable archer fish water exit.

  8. Analytic solutions of hydrodynamics equations

    Coggeshall, S.V.

    1991-01-01

    Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

  9. Rapidity correlations test stochastic hydrodynamics

    Zin, C; Gavin, S; Moschelli, G

    2017-01-01

    We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time τ π that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity ν = η/sT . We formulate methods for computing these correlations using second order dissipative hydrodynamics with noise. Current data are consistent with τ π /ν ∼ 10 but targeted measurements can improve this precision. (paper)

  10. Hydrodynamic simulations of expanding shells

    Wünsch, Richard; Palouš, Jan; Ehlerová, Soňa

    2004-01-01

    Roč. 289, 3-4 (2004), s. 35-36 ISSN 0004-640X. [From observation to self-consistent modelling of the ISM in galaxies. Porto, 03.09.2002-05.09.2002] R&D Projects: GA AV ČR KSK1048102 Keywords : hydrodynamic simulations * ISM * star formation Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 0.597, year: 2004

  11. Hydrodynamic Limit of Multiple SLE

    Hotta, Ikkei; Katori, Makoto

    2018-04-01

    Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm-Loewner evolution (SLE) as the number of slits N goes to infinity. When the N slits grow from points on the real line R in a simultaneous way and go to infinity within the upper half plane H, an ordinary differential equation describing time evolution of the conformal map g_t(z) was derived in the N → ∞ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on R studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner's semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner's semicircle law determines the time evolution of the SLE hull, K_t \\subset H\\cup R, in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from -a exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull K_t in the hydrodynamic limit.

  12. Hydrodynamical model with massless constituents

    Chiu, C.B.; Wang, K.H.

    1974-01-01

    Within the constituent hydrodynamical model, it is shown that the total number of constituents is conserved, if these constituents are massless and satisfy the Fermi-Dirac distribution. A simple scheme for the transition from the constituent-phase to the hadron-phase is suggested, and the hadron inclusive momentum spectra are presented for this case. This phase transition scheme predicts the average transverse momentum of meson resonances which is compatible with the data. (U.S.)

  13. Superconductor stability 90: A review

    Dresner, L.

    1990-01-01

    This paper reviews some recent developments in the field of stability of superconductors. The main topics dealt with are hydrodynamic phenomena in cable-in-conduit superconductors, namely, multiple stability, quench pressure, thermal expulsion, and thermal hydraulic quenchback, traveling normal zones in large, composite conductors, such as those intended for SMES, and the stability of vapor-cooled leads made of high-temperature superconductors. 31 refs., 5 figs

  14. An implicit Smooth Particle Hydrodynamic code

    Knapp, Charles E. [Univ. of New Mexico, Albuquerque, NM (United States)

    2000-05-01

    An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.

  15. Numerical Hydrodynamics in Special Relativity.

    Martí, José Maria; Müller, Ewald

    2003-01-01

    This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction. Supplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.

  16. Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

    Guercilena, Federico; Radice, David; Rezzolla, Luciano

    2017-07-01

    We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

  17. The chimera state in colloidal phase oscillators with hydrodynamic interaction

    Hamilton, Evelyn; Bruot, Nicolas; Cicuta, Pietro

    2017-12-01

    The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes. The chimera state can thus be connected to a superposition of eigenstates, whilst considering the mean interaction strength within and across subsystems allows us to make a connection to more generic (and abstract) chimeras in populations of Kuramoto phase oscillators. From this work, we expect the chimera state to emerge in experimental observations of oscillators coupled through hydrodynamic forces.

  18. Hydrodynamic Investigation of a Concentric Cylindrical OWC Wave Energy Converter

    Yu Zhou

    2018-04-01

    Full Text Available A fixed, concentric, cylindrical oscillating water column (OWC wave energy converter (WEC is proposed for shallow offshore sites. Compared with the existing shoreline OWC device, this wave energy device is not restricted by the wave directions and coastline geography conditions. Analytical solutions are derived based on the linear potential-flow theory and eigen-function expansion technique to investigate hydrodynamic properties of the device. Three typical free-surface oscillation modes in the chamber are discussed, of which the piston-type mode makes the main contribution to the energy conversion. The effects of the geometrical parameters on the hydrodynamic properties are further investigated. The resonance frequency of the chamber, the power extraction efficiency, and the effective frequency bandwidth of the device is discussed, amongst other topics. It is found that the proposed OWC-WEC device with a lower draft and wider chamber breadth has better power extraction ability.

  19. Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling.

    Hou, Yan-Hua; Yu, Zhenhua

    2015-10-20

    Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations.

  20. Kinetic theory of nonequilibrium ensembles, irreversible thermodynamics, and generalized hydrodynamics

    Eu, Byung Chan

    2016-01-01

    This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respe...

  1. CRKSPH: A new meshfree hydrodynamics method with applications to astrophysics

    Owen, John Michael; Raskin, Cody; Frontiere, Nicholas

    2018-01-01

    The study of astrophysical phenomena such as supernovae, accretion disks, galaxy formation, and large-scale structure formation requires computational modeling of, at a minimum, hydrodynamics and gravity. Developing numerical methods appropriate for these kinds of problems requires a number of properties: shock-capturing hydrodynamics benefits from rigorous conservation of invariants such as total energy, linear momentum, and mass; lack of obvious symmetries or a simplified spatial geometry to exploit necessitate 3D methods that ideally are Galilean invariant; the dynamic range of mass and spatial scales that need to be resolved can span many orders of magnitude, requiring methods that are highly adaptable in their space and time resolution. We have developed a new Lagrangian meshfree hydrodynamics method called Conservative Reproducing Kernel Smoothed Particle Hydrodynamics, or CRKSPH, in order to meet these goals. CRKSPH is a conservative generalization of the meshfree reproducing kernel method, combining the high-order accuracy of reproducing kernels with the explicit conservation of mass, linear momentum, and energy necessary to study shock-driven hydrodynamics in compressible fluids. CRKSPH's Lagrangian, particle-like nature makes it simple to combine with well-known N-body methods for modeling gravitation, similar to the older Smoothed Particle Hydrodynamics (SPH) method. Indeed, CRKSPH can be substituted for SPH in existing SPH codes due to these similarities. In comparison to SPH, CRKSPH is able to achieve substantially higher accuracy for a given number of points due to the explicitly consistent (and higher-order) interpolation theory of reproducing kernels, while maintaining the same conservation principles (and therefore applicability) as SPH. There are currently two coded implementations of CRKSPH available: one in the open-source research code Spheral, and the other in the high-performance cosmological code HACC. Using these codes we have applied

  2. Solitonic Dispersive Hydrodynamics: Theory and Observation

    Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.

    2018-04-01

    Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

  3. Annual Report: Hydrodynamics and Radiative Hydrodynamics with Astrophysical Applications

    R. Paul Drake

    2005-12-01

    We report the ongoing work of our group in hydrodynamics and radiative hydrodynamics with astrophysical applications. During the period of the existing grant, we have carried out two types of experiments at the Omega laser. One set of experiments has studied radiatively collapsing shocks, obtaining high-quality scaling data using a backlit pinhole and obtaining the first (ever, anywhere) Thomson-scattering data from a radiative shock. Other experiments have studied the deeply nonlinear development of the Rayleigh-Taylor (RT) instability from complex initial conditions, obtaining the first (ever, anywhere) dual-axis radiographic data using backlit pinholes and ungated detectors. All these experiments have applications to astrophysics, discussed in the corresponding papers either in print or in preparation. We also have obtained preliminary radiographs of experimental targets using our x-ray source. The targets for the experiments have been assembled at Michigan, where we also prepare many of the simple components. The above activities, in addition to a variety of data analysis and design projects, provide good experience for graduate and undergraduates students. In the process of doing this research we have built a research group that uses such work to train junior scientists.

  4. Hydrodynamic interactions in active colloidal crystal microrheology

    Weeber, R; Harting, JDR Jens

    2012-01-01

    In dense colloids it is commonly assumed that hydrodynamic interactions do not play a role. However, a found theoretical quantification is often missing. We present computer simulations that are motivated by experiments where a large colloidal particle is dragged through a colloidal crystal. To qualify the influence of long-ranged hydrodynamics, we model the setup by conventional Langevin dynamics simulations and by an improved scheme with limited hydrodynamic interactions. This scheme signif...

  5. Disruptive Innovation in Numerical Hydrodynamics

    Waltz, Jacob I. [Los Alamos National Laboratory

    2012-09-06

    We propose the research and development of a high-fidelity hydrodynamic algorithm for tetrahedral meshes that will lead to a disruptive innovation in the numerical modeling of Laboratory problems. Our proposed innovation has the potential to reduce turnaround time by orders of magnitude relative to Advanced Simulation and Computing (ASC) codes; reduce simulation setup costs by millions of dollars per year; and effectively leverage Graphics Processing Unit (GPU) and future Exascale computing hardware. If successful, this work will lead to a dramatic leap forward in the Laboratory's quest for a predictive simulation capability.

  6. Hydrodynamics of post CHF region

    Ishii, M.; De Jarlais, G.

    1984-04-01

    Among various two-phase flow regimes, the inverted flow in the post-dryout region is relatively less well understood due to its special heat transfer conditions. The review of existing data indicates further research is needed in the areas of basic hydrodynamics related to liquid core disintegration mechanisms, slug and droplet formations, entrainment, and droplet size distributions. In view of this, the inverted flow is studied in detail both analytically and experimentally. Criteria for initial flow regimes in the post-dryout region are given. Preliminary models for subsequent flow regime transition criteria are derived together with correlations for a mean droplet diameter based on the adiabatic simulation data

  7. Problems in astrophysical radiation hydrodynamics

    Castor, J.I.

    1983-01-01

    The basic equations of radiation hydrodynamics are discussed in the regime that the radiation is dynamically as well as thermally important. Particular attention is paid to the question of what constitutes an acceptable approximate non-relativistic system of dynamical equations for matter and radiation in this regime. Further discussion is devoted to two classes of application of these ideas. The first class consists of problems dominated by line radiation, which is sensitive to the velocity field through the Doppler effect. The second class is of problems in which the advection of radiation by moving matter dominates radiation diffusion

  8. Hydrodynamics and stellar winds an introduction

    Maciel, Walter J

    2014-01-01

    Stellar winds are a common phenomenon in the life of stars, from the dwarfs like the Sun to the red giants and hot supergiants, constituting one of the basic aspects of modern astrophysics. Stellar winds are a hydrodynamic phenomenon in which circumstellar gases expand towards the interstellar medium. This book presents an elementary introduction to the fundamentals of hydrodynamics with an application to the study of stellar winds. The principles of hydrodynamics have many other applications, so that the book can be used as an introduction to hydrodynamics for students of physics, astrophysics and other related areas.

  9. Hydrodynamic interactions in active colloidal crystal microrheology.

    Weeber, R; Harting, J

    2012-11-01

    In dense colloids it is commonly assumed that hydrodynamic interactions do not play a role. However, a found theoretical quantification is often missing. We present computer simulations that are motivated by experiments where a large colloidal particle is dragged through a colloidal crystal. To qualify the influence of long-ranged hydrodynamics, we model the setup by conventional Langevin dynamics simulations and by an improved scheme with limited hydrodynamic interactions. This scheme significantly improves our results and allows to show that hydrodynamics strongly impacts the development of defects, the crystal regeneration, as well as the jamming behavior.

  10. Genetic analyses using GGE model and a mixed linear model approach, and stability analyses using AMMI bi-plot for late-maturity alpha-amylase activity in bread wheat genotypes.

    Rasul, Golam; Glover, Karl D; Krishnan, Padmanaban G; Wu, Jixiang; Berzonsky, William A; Fofana, Bourlaye

    2017-06-01

    Low falling number and discounting grain when it is downgraded in class are the consequences of excessive late-maturity α-amylase activity (LMAA) in bread wheat (Triticum aestivum L.). Grain expressing high LMAA produces poorer quality bread products. To effectively breed for low LMAA, it is necessary to understand what genes control it and how they are expressed, particularly when genotypes are grown in different environments. In this study, an International Collection (IC) of 18 spring wheat genotypes and another set of 15 spring wheat cultivars adapted to South Dakota (SD), USA were assessed to characterize the genetic component of LMAA over 5 and 13 environments, respectively. The data were analysed using a GGE model with a mixed linear model approach and stability analysis was presented using an AMMI bi-plot on R software. All estimated variance components and their proportions to the total phenotypic variance were highly significant for both sets of genotypes, which were validated by the AMMI model analysis. Broad-sense heritability for LMAA was higher in SD adapted cultivars (53%) compared to that in IC (49%). Significant genetic effects and stability analyses showed some genotypes, e.g. 'Lancer', 'Chester' and 'LoSprout' from IC, and 'Alsen', 'Traverse' and 'Forefront' from SD cultivars could be used as parents to develop new cultivars expressing low levels of LMAA. Stability analysis using an AMMI bi-plot revealed that 'Chester', 'Lancer' and 'Advance' were the most stable across environments, while in contrast, 'Kinsman', 'Lerma52' and 'Traverse' exhibited the lowest stability for LMAA across environments.

  11. Invariant description of solutions of hydrodynamic-type systems in hodograph space: hydrodynamic surfaces

    Ferapontov, E.V.

    2002-01-01

    Hydrodynamic surfaces are solutions of hydrodynamic-type systems viewed as non-parametrized submanifolds of the hodograph space. We propose an invariant differential-geometric characterization of hydrodynamic surfaces by expressing the curvature form of the characteristic web in terms of the reciprocal invariants. (author)

  12. An introduction to relativistic hydrodynamics

    Font, Jose A [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)

    2007-11-15

    We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, particularly within the test-fluid approximation but also for dynamical spacetimes. While such advances also hold true in the case of the MHD equations, the astrophysical applications investigated so far are still limited, yet the field is bound to witness major developments in the near future. The article also presents a brief overview of numerical techniques, providing state-of-the-art examples of their applicability to general relativistic fluids and magneto-fluids in characteristic scenarios of relativistic astrophysics.

  13. Inducer Hydrodynamic Load Measurement Devices

    Skelley, Stephen E.; Zoladz, Thomas F.

    2002-01-01

    Marshall Space Flight Center (MSFC) has demonstrated two measurement devices for sensing and resolving the hydrodynamic loads on fluid machinery. The first - a derivative of the six component wind tunnel balance - senses the forces and moments on the rotating device through a weakened shaft section instrumented with a series of strain gauges. This "rotating balance" was designed to directly measure the steady and unsteady hydrodynamic loads on an inducer, thereby defining both the amplitude and frequency content associated with operating in various cavitation modes. The second device - a high frequency response pressure transducer surface mounted on a rotating component - was merely an extension of existing technology for application in water. MSFC has recently completed experimental evaluations of both the rotating balance and surface-mount transducers in a water test loop. The measurement bandwidth of the rotating balance was severely limited by the relative flexibility of the device itself, resulting in an unexpectedly low structural bending mode and invalidating the higher frequency response data. Despite these limitations, measurements confirmed that the integrated loads on the four-bladed inducer respond to both cavitation intensity and cavitation phenomena. Likewise, the surface-mount pressure transducers were subjected to a range of temperatures and flow conditions in a non-rotating environment to record bias shifts and transfer functions between the transducers and a reference device. The pressure transducer static performance was within manufacturer's specifications and dynamic response accurately followed that of the reference.

  14. CHASM Challenge Problem: Lagrangian Hydrodynamics

    Hornung, R [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Keasler, J [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gokhale, M [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2010-09-10

    Computer simulations of many science and engineering problems require modeling the equations of hydrodynamics which describe the motion of materials relative to each other induced by various forces. Many important DoD simulation problems involve complex multi-material systems that undergo large deformations. Examples include the analysis of armor defense, penetration mechanics, blast effects, structural integrity, and conventional munitions such as shaped charges and explosively formed projectiles. Indeed, the original motivation for developing codes that solve the equations of hydrodynamics, herein referred to as “hydrocodes”, was to solve problems with defense applications. The FY2010 Requirements Analysis Report issued by the DoD High Performance Computing Modernization Program (HPCMP) Office shows that a major portion of DoD HPC activities involves hydrocodes [HPCMP2010]. The report surveyed 496 projects across the Services and various Agencies, representing 4,050 HPCMP users at more than 125 locations, including government, contractors, and academia, and grouped each project into one of ten categories.

  15. Linear gate

    Suwono.

    1978-01-01

    A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)

  16. June Solstice Equatorial Spread F in the American Sector: A Numerical Assessment of Linear Stability Aided by Incoherent Scatter Radar Measurements

    Zhan, Weijia; S. Rodrigues, Fabiano

    2018-01-01

    Previous studies have suggested that weakening downward plasma drifts can produce favorable conditions for the ionospheric Generalized Rayleigh-Taylor (GRT) instability and explain the occurrence of postmidnight equatorial spread F (ESF). We evaluated this hypothesis using numerical simulations aided by measurements and attempted to explain ESF events observed in the American sector during June solstice, low solar flux conditions. We analyzed plasma drifts and ESF measurements made by the incoherent scatter radar of the Jicamarca Radio Observatory (11.95° S, 76.87° W, ˜1° dip). We found adequate measurements during a prototypical, quiet time event on 4-5 June 2008 when the downward drifts weakened and a fully developed ESF appeared. The measured drifts were used as input for the SAMI2 model. SAMI2 reproduced an "apparent" uplift of the ionosphere based on h'F measurements that was consistent with expectations and observations. SAMI2 also provided parameters for estimation of the flux tube linear growth rates of GRT instability associated with the weakening drift event. We found that the weakening drifts did produce unstable conditions with positive growth rates. The growth rates, however, were slower than those obtained for typical, premidnight ESF events and those obtained for similar drift conditions in other longitude sectors. We show, however, that departures in the wind pattern, from climatological model predictions, can produce favorable conditions for instability development. Following the hypothesis of Huba and Krall (2013) and using SAMI2 simulations, we show that equatorward winds, when combined with weakening drifts, could have contributed to the unstable conditions responsible for the postmidnight ESF events.

  17. Linear Accelerators

    Vretenar, M

    2014-01-01

    The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics

  18. Hydrodynamic description of spin Calogero-Sutherland model

    Abanov, Alexander; Kulkarni, Manas; Franchini, Fabio

    2009-03-01

    We study a non-linear collective field theory for an integrable spin-Calogero-Sutherland model. The hydrodynamic description of this SU(2) model in terms of charge density, charge velocity and spin currents is used to study non-perturbative solutions (solitons) and examine their correspondence with known quantum numbers of elementary excitations [1]. A conventional linear bosonization or harmonic approximation is not sufficient to describe, for example, the physics of spin-charge (non)separation. Therefore, we need this new collective bosonic field description that captures the effects of the band curvature. In the strong coupling limit [2] this model reduces to integrable SU(2) Haldane-Shastry model. We study a non-linear coupling of left and right spin currents which form a Kac-Moody algebra. Our quantum hydrodynamic description for the spin case is an extension for the one found in the spinless version in [3].[3pt] [1] Y. Kato,T. Yamamoto, and M. Arikawa, J. Phys. Soc. Jpn. 66, 1954-1961 (1997).[0pt] [2] A. Polychronakos, Phys Rev Lett. 70,2329-2331(1993).[0pt] [3] A.G.Abanov and P.B. Wiegmann, Phys Rev Lett 95, 076402(2005)

  19. Linearization Method and Linear Complexity

    Tanaka, Hidema

    We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

  20. Hydrodynamic and hydromagnetic stability of black holes with ...

    ... research career – radiative transfer, magnetohydrodynamics and black holes .... icant parts of a jet that happen to maximize the Lorentz factor while including us ... The choice for the momentum carrier is between electromagnetic field and ..... possible to understand, at least qualitatively, the influence of black hole spin and.

  1. Can numerical simulations accurately predict hydrodynamic instabilities in liquid films?

    Denner, Fabian; Charogiannis, Alexandros; Pradas, Marc; van Wachem, Berend G. M.; Markides, Christos N.; Kalliadasis, Serafim

    2014-11-01

    Understanding the dynamics of hydrodynamic instabilities in liquid film flows is an active field of research in fluid dynamics and non-linear science in general. Numerical simulations offer a powerful tool to study hydrodynamic instabilities in film flows and can provide deep insights into the underlying physical phenomena. However, the direct comparison of numerical results and experimental results is often hampered by several reasons. For instance, in numerical simulations the interface representation is problematic and the governing equations and boundary conditions may be oversimplified, whereas in experiments it is often difficult to extract accurate information on the fluid and its behavior, e.g. determine the fluid properties when the liquid contains particles for PIV measurements. In this contribution we present the latest results of our on-going, extensive study on hydrodynamic instabilities in liquid film flows, which includes direct numerical simulations, low-dimensional modelling as well as experiments. The major focus is on wave regimes, wave height and wave celerity as a function of Reynolds number and forcing frequency of a falling liquid film. Specific attention is paid to the differences in numerical and experimental results and the reasons for these differences. The authors are grateful to the EPSRC for their financial support (Grant EP/K008595/1).

  2. Hydrodynamic Overview at Hot Quarks 2016

    Noronha-Hostler, Jacquelyn

    2017-01-01

    Event-by-event relativistic hydrodynamics has been extremely successful in describing flow observables in heavy-ion collisions. However, the initial state and viscosity simultaneously affect comparisons to data so a discussion of experimental observables that help to distinguish the two follows. Specific problems that arise in the hydrodynamical modeling at the Beam Energy Scan are also addressed. (paper)

  3. Two-fluid hydrodynamic model for semiconductors

    Maack, Johan Rosenkrantz; Mortensen, N. Asger; Wubs, Martijn

    2018-01-01

    The hydrodynamic Drude model (HDM) has been successful in describing the optical properties of metallic nanostructures, but for semiconductors where several different kinds of charge carriers are present an extended theory is required. We present a two-fluid hydrodynamic model for semiconductors...

  4. Experimental investigation of hydrodynamic cavitation through orifices of different geometries

    Rudolf, Pavel; Kubina, Dávid; Hudec, Martin; Kozák, Jiří; Maršálek, Blahoslav; Maršálková, Eliška; Pochylý, František

    Hydrodynamic cavitation in single and multihole orifices was experimentally investigated to assess their hydraulic characteristics: loss coefficients, inception cavitation number, cavitation number for transition to supercavitation. Significant difference for singlehole and multihole orifices was observed in terms of the measured loss coefficient. It is significantly more effective to use multihole orifices, where energy dissipation is much lower.It was found that using scaling factor given by ratio of orifice thickness suggests linear behaviour of both loss coefficient and inception cavitation number. Orifices seem to be convenient choice as flow constriction devices inducing cavitation due to their simplicity.

  5. Experimental investigation of hydrodynamic cavitation through orifices of different geometries

    Rudolf Pavel

    2017-01-01

    Full Text Available Hydrodynamic cavitation in single and multihole orifices was experimentally investigated to assess their hydraulic characteristics: loss coefficients, inception cavitation number, cavitation number for transition to supercavitation. Significant difference for singlehole and multihole orifices was observed in terms of the measured loss coefficient. It is significantly more effective to use multihole orifices, where energy dissipation is much lower.It was found that using scaling factor given by ratio of orifice thickness suggests linear behaviour of both loss coefficient and inception cavitation number. Orifices seem to be convenient choice as flow constriction devices inducing cavitation due to their simplicity.

  6. Hydrodynamic limit of a nongradient interacting particle process

    Wick, W.D.

    1989-01-01

    A simple example of a nongradient stochastic interacting particle system is analyzed. In this model, symmetric simple exclusion in one dimension in a periodic environment, the dynamical term in the Green-Kubo formula contributes to the bulk diffusion constant. The law of large numbers for the density field and the central limit theorem for the density fluctuation field are proven, and the Green-Kubo expression for the diffusion constant is computed exactly. The hydrodynamic equation for the model turns out to be linear

  7. Linear algebra

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  8. Hemolytic potential of hydrodynamic cavitation.

    Chambers, S D; Bartlett, R H; Ceccio, S L

    2000-08-01

    The purpose of this study was to determine the hemolytic potentials of discrete bubble cavitation and attached cavitation. To generate controlled cavitation events, a venturigeometry hydrodynamic device, called a Cavitation Susceptibility Meter (CSM), was constructed. A comparison between the hemolytic potential of discrete bubble cavitation and attached cavitation was investigated with a single-pass flow apparatus and a recirculating flow apparatus, both utilizing the CSM. An analytical model, based on spherical bubble dynamics, was developed for predicting the hemolysis caused by discrete bubble cavitation. Experimentally, discrete bubble cavitation did not correlate with a measurable increase in plasma-free hemoglobin (PFHb), as predicted by the analytical model. However, attached cavitation did result in significant PFHb generation. The rate of PFHb generation scaled inversely with the Cavitation number at a constant flow rate, suggesting that the size of the attached cavity was the dominant hemolytic factor.

  9. Deterministic hydrodynamics: Taking blood apart

    Davis, John A.; Inglis, David W.; Morton, Keith J.; Lawrence, David A.; Huang, Lotien R.; Chou, Stephen Y.; Sturm, James C.; Austin, Robert H.

    2006-10-01

    We show the fractionation of whole blood components and isolation of blood plasma with no dilution by using a continuous-flow deterministic array that separates blood components by their hydrodynamic size, independent of their mass. We use the technology we developed of deterministic arrays which separate white blood cells, red blood cells, and platelets from blood plasma at flow velocities of 1,000 μm/sec and volume rates up to 1 μl/min. We verified by flow cytometry that an array using focused injection removed 100% of the lymphocytes and monocytes from the main red blood cell and platelet stream. Using a second design, we demonstrated the separation of blood plasma from the blood cells (white, red, and platelets) with virtually no dilution of the plasma and no cellular contamination of the plasma. cells | plasma | separation | microfabrication

  10. The hydrodynamic theory of detonation

    Langweiler, Heinz

    1939-01-01

    This report derives equations containing only directly measurable constants for the quantities involved in the hydrodynamic theory of detonation. The stable detonation speed, D, is revealed as having the lowest possible value in the case of positive material velocity, by finding the minimum of the Du curve (u denotes the speed of the gases of combustion). A study of the conditions of energy and impulse in freely suspended detonating systems leads to the disclosure of a rarefaction front traveling at a lower speed behind the detonation front; its velocity is computed. The latent energy of the explosive passes into the steadily growing detonation zone - the region between the detonation front and the rarefaction front. The conclusions lead to a new definition of the concept of shattering power. The calculations are based on the behavior of trinitrotoluene.

  11. Fluctuating nonlinear hydrodynamics of flocking

    Yadav, Sunil Kumar; Das, Shankar P.

    2018-03-01

    Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.

  12. Hydrodynamics and phases of flocks

    Toner, John; Tu Yuhai; Ramaswamy, Sriram

    2005-01-01

    We review the past decade's theoretical and experimental studies of flocking: the collective, coherent motion of large numbers of self-propelled 'particles' (usually, but not always, living organisms). Like equilibrium condensed matter systems, flocks exhibit distinct 'phases' which can be classified by their symmetries. Indeed, the phases that have been theoretically studied to date each have exactly the same symmetry as some equilibrium phase (e.g., ferromagnets, liquid crystals). This analogy with equilibrium phases of matter continues in that all flocks in the same phase, regardless of their constituents, have the same 'hydrodynamic'-that is, long-length scale and long-time behavior, just as, e.g., all equilibrium fluids are described by the Navier-Stokes equations. Flocks are nonetheless very different from equilibrium systems, due to the intrinsically nonequilibrium self-propulsion of the constituent 'organisms'. This difference between flocks and equilibrium systems is most dramatically manifested in the ability of the simplest phase of a flock, in which all the organisms are, on average moving in the same direction (we call this a 'ferromagnetic' flock; we also use the terms 'vector-ordered' and 'polar-ordered' for this situation) to exist even in two dimensions (i.e., creatures moving on a plane), in defiance of the well-known Mermin-Wagner theorem of equilibrium statistical mechanics, which states that a continuous symmetry (in this case, rotation invariance, or the ability of the flock to fly in any direction) can not be spontaneously broken in a two-dimensional system with only short-ranged interactions. The 'nematic' phase of flocks, in which all the creatures move preferentially, or are simply oriented preferentially, along the same axis, but with equal probability of moving in either direction, also differs dramatically from its equilibrium counterpart (in this case, nematic liquid crystals). Specifically, it shows enormous number fluctuations, which

  13. Anomalous hydrodynamics kicks neutron stars

    Kaminski, Matthias, E-mail: mski@ua.edu [Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487 (United States); Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8P 5C2 (Canada); Uhlemann, Christoph F. [Department of Physics, University of Washington, Seattle, WA 98195 (United States); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Goethe-Universität Frankfurt (Germany); Institut für Theoretische Physik, Goethe Universität Frankfurt (Germany); Schaffner-Bielich, Jürgen [Institut für Theoretische Physik, Goethe Universität Frankfurt (Germany)

    2016-09-10

    Observations show that, at the beginning of their existence, neutron stars are accelerated briskly to velocities of up to a thousand kilometers per second. We argue that this remarkable effect can be explained as a manifestation of quantum anomalies on astrophysical scales. To theoretically describe the early stage in the life of neutron stars we use hydrodynamics as a systematic effective-field-theory framework. Within this framework, anomalies of the Standard Model of particle physics as underlying microscopic theory imply the presence of a particular set of transport terms, whose form is completely fixed by theoretical consistency. The resulting chiral transport effects in proto-neutron stars enhance neutrino emission along the internal magnetic field, and the recoil can explain the order of magnitude of the observed kick velocities.

  14. Hydrodynamic dispersion within porous biofilms

    Davit, Y.

    2013-01-23

    Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher\\'s equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels\\' network; (2) the solute\\'s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport. © 2013 American Physical Society.

  15. Biomimetic shark skin: design, fabrication and hydrodynamic function.

    Wen, Li; Weaver, James C; Lauder, George V

    2014-05-15

    Although the functional properties of shark skin have been of considerable interest to both biologists and engineers because of the complex hydrodynamic effects of surface roughness, no study to date has successfully fabricated a flexible biomimetic shark skin that allows detailed study of hydrodynamic function. We present the first study of the design, fabrication and hydrodynamic testing of a synthetic, flexible, shark skin membrane. A three-dimensional (3D) model of shark skin denticles was constructed using micro-CT imaging of the skin of the shortfin mako (Isurus oxyrinchus). Using 3D printing, thousands of rigid synthetic shark denticles were placed on flexible membranes in a controlled, linear-arrayed pattern. This flexible 3D printed shark skin model was then tested in water using a robotic flapping device that allowed us to either hold the models in a stationary position or move them dynamically at their self-propelled swimming speed. Compared with a smooth control model without denticles, the 3D printed shark skin showed increased swimming speed with reduced energy consumption under certain motion programs. For example, at a heave frequency of 1.5 Hz and an amplitude of ± 1 cm, swimming speed increased by 6.6% and the energy cost-of-transport was reduced by 5.9%. In addition, a leading-edge vortex with greater vorticity than the smooth control was generated by the 3D printed shark skin, which may explain the increased swimming speeds. The ability to fabricate synthetic biomimetic shark skin opens up a wide array of possible manipulations of surface roughness parameters, and the ability to examine the hydrodynamic consequences of diverse skin denticle shapes present in different shark species. © 2014. Published by The Company of Biologists Ltd.

  16. Enhanced decolorization of methyl orange using zero-valent copper nanoparticles under assistance of hydrodynamic cavitation.

    Li, Pan; Song, Yuan; Wang, Shuai; Tao, Zheng; Yu, Shuili; Liu, Yanan

    2015-01-01

    The rate of reduction reactions of zero-valent metal nanoparticles is restricted by their agglomeration. Hydrodynamic cavitation was used to overcome the disadvantage in this study. Experiments for decolorization of methyl orange azo dye by zero-valent copper nanoparticles were carried out in aqueous solution with and without hydrodynamic cavitation. The results showed that hydrodynamic cavitation greatly accelerated the decolorization rate of methyl orange. The size of nanoparticles was decreased after hydrodynamic cavitation treatment. The effects of important operating parameters such as discharge pressure, initial solution pH, and copper nanoparticle concentration on the degradation rates were studied. It was observed that there was an optimum discharge pressure to get best decolorization performance. Lower solution pH were favorable for the decolorization. The pseudo-first-order kinetic constant for the degradation of methyl orange increased linearly with the copper dose. UV-vis spectroscopic and Fourier transform infrared (FT-IR) analyses confirmed that many degradation intermediates were formed. The results indicated hydroxyl radicals played a key role in the decolorization process. Therefore, the enhancement of decolorization by hydrodynamic cavitation could due to the deagglomeration of nanoparticles as well as the oxidation by the in situ generated hydroxyl radicals. These findings greatly increase the potential of the Cu(0)/hydrodynamic cavitation technique for use in the field of treatment of wastewater containing hazardous materials. Copyright © 2014 Elsevier B.V. All rights reserved.

  17. Soliton shock wave fronts and self-similar discontinuities in dispersion hydrodynamics

    Gurevich, A.V.; Meshcherkin, A.P.

    1987-01-01

    Nonlinear flows in nondissipative dispersion hydrodynamics are examined. It is demonstrated that in order to describe such flows it is necessary to incorporate a new concept: a special discontinuity called a ''self-similar'' discontinuity consisting of a nondissipative shock wave and a powerful slow wave discontinuity in regular hydrodynamics. The ''self similar discontinuity'' expands linearly over time. It is demonstrated that this concept may be introduced in a solution to Euler equations. The boundary conditions of the ''self similar discontinuity'' that allow closure of Euler equations for dispersion hydrodynamics are formulated, i.e., those that replace the shock adiabatic curve of standard dissipative hydrodynamics. The structure of the soliton front and of the trailing edge of the shock wave is investigated. A classification and complete solution are given to the problem of the decay of random initial discontinuities in the hydrodynamics of highly nonisothermic plasma. A solution is derived to the problem of the decay of initial discontinuities in the hydrodynamics of magnetized plasma. It is demonstrated that in this plasma, a feature of current density arises at the point of soliton inversion

  18. Modeling hydrodynamic instabilities of double ablation fronts in inertial confinement fusion

    Yanez, C.; Sanz, J.; Olazabal-Loume, M.; Ibanez, L. F.

    2013-01-01

    A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations. (authors)

  19. Linear algebra

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  20. Linear programming

    Solow, Daniel

    2014-01-01

    This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.