Showing papers on "Dissipative system published in 1974"
TL;DR: In this paper, the dynamics and stability of flexible pipes containing flowing fluid are examined in a general way and it is shown that conservative systems are subject not only to buckling (divergence) at sufficiently high flow velocities, but also to oscillatory instabilities (flutter) at higher flow velocity.
518 citations
TL;DR: In this paper, a model of elastic energy dissipation based on a memory mechanism with two degrees of freedom is applied to the problem of the determination of the response spectrum at the surface of a layer when the spectrum is given at the bottom.
Abstract: A model of elastic‐energy dissipation based on a memory mechanism with two degrees of freedom is applied to the problem of the determination of the response spectrum at the surface of a layer when the spectrum is given at the bottom. The reaction of the surface of the layer is obtained directly with the Laplace‐transform method. With the Fourier method, the amplification function is also found at the surface of the layer; it depends on the first power of the coefficient of viscosity—the Q−1 is proportional to a fractional power of the frequency. The reaction inside of the layer in the case of an infinite layer has also been obtained as function of time and in the Fourier space. It is verified that the amplification function (namely, the peak amplitude response of the free surface of the viscoelastic layer at a “resonant frequency”) depends strongly on the dissipation mechanism; a complete knowledge of the parameters of this mechanism could be of great help in the solution of many physical and engineering ...
242 citations
TL;DR: In this paper, the authors investigate the effects of localized nonlinear reaction sites, such as electrode surfaces or catalytic membranes, on an otherwise stable reacting-diffusing bulk medium and obtain an integral equation as the formal solution of the partial differential equations describing reaction and diffusion in the total system, in which the nonlinearities of the local reaction sites are fully retained.
Abstract: We investigate some far‐from‐equilibrium effects of localized nonlinear reaction sites, such as electrode surfaces or catalytic membranes, on an otherwise stable reacting‐diffusing bulk medium. We obtain an integral equation as the formal solution of the partial differential equations describing reaction and diffusion in the total system, in which the nonlinearities of the local reaction sites are fully retained; the kernel of that integral equation is a propagator function which describes the linearized bulk dynamics in the absence of the localized reactions. Analytical solutions to the integral equations are found for several mechanisms which demonstrate the existence of a variety of typically far‐from‐equilibrium phenomena. The equations for steady states are derived and used to show the existence of multiple steady states for a model system. A determinantal condition for the stability of steady states is obtained and applied to another model system consisting of a localization of the Prigogine‐Lefever mechanism with no bulk reactions. The system is found to have oscillatory instability whose frequency depends on transport processes in the bulk as well as on the parameters of the localized reactions. Waves and dissipative space structures on a planar localized reaction site are shown to obey ordinary integral equations which are solved, in the case of waves, for two model cases. The waves are shown to exist only in a region about the plane of the local reaction. Propagation occurs due to bulk transport processes coupling both local and bulk reaction in the vicinity of the reactive surface. Waves are shown to propagate along the membrane or surface only for certain ranges of values of the wavevector. A threshold wave phenomenon is shown to exist for one case, such that over the entire range of allowed wavevectors waves exist only beyond a minimal amplitude about a stable steady state. Symmetry‐breaking instabilities in a system with two equivalent localized sites are considered and we show that these can occur only for intermediate values of separation of the local sites.
78 citations
TL;DR: A model chemical network involving reactions and diffusion is studied, and spatially and temporally ordered solutions of the equations are found by bifurcation theory.
Abstract: A model chemical network involving reactions and diffusion is studied Spatially and temporally ordered solutions of the equations are found by bifurcation theory These solutions are calculated analytically and their stability is studied Properties of these dissipative structures are discussed, and a comparison with Thom's theories of morphogenesis is outlined
64 citations
TL;DR: In this paper, a rigorous hydrodynamic theory is presented which is formulated and derived, from the start, in terms of measurable correlation functions, and applied easily also to other ordered systems like glasses, isotropic ferro-and antiferromagnets, superfluids, and, of course, normal fluids.
59 citations
01 Jan 1974
TL;DR: In this paper, a connection between dissipative finite difference operators and a Galerkin-type method for numerical solution of first order one-dimensional hyperbolic problems is discussed.
Abstract: Publisher Summary This chapter focuses on connection between dissipative finite difference operators and a certain Galerkin-type method, for the numerical solution of first order one-dimensional hyperbolic problems, and discusses the extension of the Galerkin method to certain equations that are of third order in the space derivative It also discusses the question of the accuracy in L 2 of the ordinary Galerkin method The chapter also discusses the dissipativity of the Galerkin operator and discussion on higher order education
46 citations
TL;DR: In this article, nonlinear internal gravity waves in a slightly dissipative, slightly compressible fluid are discussed for the case when the properties of the medium vary slowly on a scale determined by the local w...
Abstract: Nonlinear internal gravity waves in a slightly dissipative, slightly compressible fluid are discussed for the case when the properties of the medium vary slowly on a scale determined by the local w...
33 citations
TL;DR: In this paper, it was shown that elastic energy can be accumulated only through a decrease of conformational entropy, and the general thermodynamic theory for non-linear viscoelastic materials simplifies considerably.
Abstract: Polymer solutions and melts can both dissipate mechanical energy in flow, as well as accumulate elastic energy. If the assumption is made that elastic energy can be accumulated only through a decrease of conformational entropy, the general thermodynamic theory for non-linear viscoelastic materials simplifies considerably. In particular, though no generality is lost as far as the constitutive equation for stress is concerned, the energy equation, which allows in principle a calculation of temperature distributions arising from frictional heating and heat removal, reduces to the usual form which is valid for viscous materials.
32 citations
TL;DR: In this article, a one-dimensional system which exhibits a chemical instability with respect to free diffusion is analyzed numerically, and the results are used to present a model for a chemical signal to initiate cell division.
Abstract: A one‐dimensional system which exhibits a chemical instability with respect to free diffusion is analyzed numerically. Below a critical size the homogeneous state is stable. Above this size a succession of inhomogeneous states appear, each one stable over a range of values for the dimension of the system. A plot of the rate of entropy production for the system versus the dimension of the system is monotone increasing but with a change in slope at the appearance of the first inhomogeneous steady state. Transitions between inhomogeneous steady states result in a step increase in the rate of entropy production. At least one additional series of steady states is stable for the system. The results are used to present a model for a chemical signal to initiate cell division.
31 citations
TL;DR: In this article, a numerical integration of the Vlasov equation replaces the continuous eigenvalue spectrum of the problem by a discrete spectrum, which can be represented by the eigen value spectrum of a finite matrix.
23 citations
TL;DR: In this paper, a nonlinear master equation describing the nucleation of critical fluctuations leading to an instability and subsequently to a dissipative structure is derived, and it is suggested that the formation of these structures bears strong analogies with first order phase transitions.
TL;DR: The key idea of conservative Hamiltonian systems is the fact that the closed line integral of action is an absolute invariant of the motion as discussed by the authors, and the conditions required for the validity of the Liouville theorem with respect to conformal Hamiltonian flows are examined.
Abstract: The key idea of conservative Hamiltonian systems is the fact that the closed line integral of action is an absolute invariant of the motion. Dissipation effects may be included by considering those systems for which the closed integral of action is a parameter‐dependent, conformal invariant of the motion. An application of this idea to hydrodynamics is made, and the conditions required for the validity of the Liouville theorem with respect to conformal Hamiltonian flows are examined.
TL;DR: In this paper, a model of a distributed-boundary control system is considered, where the uncontrolled system possesses an exponential asymptotically stable zero solution, and the authors construct suboptimal feedback controls for the distributed and boundary control problems via the direct method of Liapunov.
TL;DR: In this paper, a new discrete mode that satisfies the radiation condition was found for the problem of a horizontal wire above an air-earth interface, which exhibits the nature of a fast wave and has a much smaller attenuation constant than the quasi-TEM mode.
Abstract: A new discrete mode that satisfies the radiation condition is found for the problem of a horizontal wire above an air-earth interface. It can be shown to be an important part of the total current distribution on the wire. It exhibits the nature of a fast wave and has a much smaller attenuation constant than the quasi-TEM mode.
01 Jan 1974
TL;DR: In this paper, a nonstandard continuous-in-time Galerkin method based on piecewise polynomial spaces is applied to the periodic initial value problem for the équation = a(x, ty u)ux + ƒ(*, ty «).
Abstract: — À nonstandard continuous-in-time Galerkin method, based on piecewise polynomial spaces, is applied io the periodic initial value problem for the équation ut = a(x, ty u)ux + ƒ(*, ty «). Under the condition that a(x, t, u) > «o > 0 for the solution, optimal order L error estimâtes are derived.
TL;DR: In this article, conditions for the onset of dissipative trapped-ion instability in tokamaks with elliptic and circular cross sections are determined, and the results show that the ions trapped in regions of good gradient contribute to the Landau damping of the unstable waves, and that ion collisional damping is also enhanced when the drifts are taken into account.
Abstract: Conditions for the onset of the dissipative trapped‐ion instability in tokamaks with elliptic and circular cross sections are determined. Toroidal gradient drifts, ignored in earlier calculations, are included in the analysis and found to give rise to significant stabilizing effects. In particular, the results show that the ions trapped in regions of good gradient (dB/dρ > 0) contribute to the Landau damping of the unstable waves, and that ion collisional damping is also enhanced when the drifts are taken into account. Since vertical ellipticity increases the region of good gradient, these stabilizing effects are further enhanced in elliptical cross‐section tokamaks. It is also shown that previously calculated restrictions on the allowable magnitude of temperature gradients for favorable damping can be relaxed. Results of the analysis are applied to expected parameters for the Princeton Large Torus experiment and growth rate estimates given for conditions violating the stability criteria.
TL;DR: In this paper, a perturbation theory is developed for a system of equations which, when linearized, has a plane wave solution with complex frequency of a small imaginary part, and the governing equation for the amplitude becomes a type of generalized nonlinear Schrodinger equation in three dimensions.
Abstract: Modulation of a nonlinear wave in a dissipative and dispersive medium is considered by the method of multiple scales. The slow variables for the amplitude are determined by the coupling between the nonlinearity of the envelope wave and the dissipative or dispersive effect. A perturbation theory is developed for a system of equations which, when linearized, has a plane wave solution with complex frequency of a small imaginary part. Governing equation for the amplitude becomes a type of generalized nonlinear Schrodinger equation in three dimensions. For spatially periodic case, there may be the case that small dissipation can make the wave grow depending on the initial amplitude. As an illustrative example of the general theory, modulation of the convective mode in a fluid layer heated from below is considered.
TL;DR: In this paper, an appropriate path differential measure is employed for obtaining the path integral representation of the propagator of a particle with a time dependent "mass", which is restricted to quadratic Lagrangians.
Abstract: An appropriate path differential measure is employed for obtaining the path integral representation of the propagator of a particle with a time dependent 'mass'. The evaluations are restricted to quadratic Lagrangians and the propagator for the damped harmonic oscillator is given explicitly.
TL;DR: In this article, a one-dimensional non-linear treatment of the electron density fluctuation is formulated based upon electron heat conduction as dissipative mechanism, and the condition for the existence of periodic solutions to the differential equation so obtained is derived to show correspondence with linear analyses.
Abstract: Discharges perpendicular to external magnetic fields in alkali-seeded noble gases lead to the formation of a well-defined electron density wave-pattern above a certain critical magnetic field strength. A one-dimensional non-linear treatment of the electron density fluctuation is formulated based upon electron heat conduction as dissipative mechanism. The condition for the existence of periodic solutions to the differential equation so obtained is derived to show correspondence with linear analyses. For not too large density fluctuations an analytic expression for the characteristic wavelength is obtainable, while stronger inhomogeneities are treated numerically. Methods for determining the wave amplitude are discussed briefly.
TL;DR: In this paper, a relatively simple analytic formula is derived for the current in a bare conducting cylinder of length 2h and radius a when embedded in an isotropic homogeneous dissipative medium and excited by a periodic electric field with uniform amplitude and phase along its axis.
Abstract: A relatively simple analytic formula is derived for the current in a bare conducting cylinder of length 2h and radius a when embedded in an isotropic homogeneous dissipative medium and excited by a periodic electric field with uniform amplitude and phase along its axis. In the derivation the same approximations are made as in an earlier analysis of the center-driven antenna for which complete experimental verification has been obtained. Computations are reported specifically for an antenna immersed in the ocean and excited by a field of very low frequency. The principal parameter is h/\lambda in the range from 0.03 to 0.23 at a frequency of 5 Hz, where \lambda is the wavelength in sea water. The effect of changes in the radius a are also shown successively with a/\lambda and h/a as the variable parameter. When the results of this paper are combined with those for the center-driven element, they provide the means for determining the response of a center-loaded dipole receiving antenna when immersed in a dissipative medium. Such an antenna is of interest in problems that relate to communication with submerged submarines and off-shore facilities.
TL;DR: In this article, second-and third-order finite-difference methods were applied to the model advection equation cast in conservative form, and the results indicated that the third order method using minimum dispersion is the most accurate method tested.
Abstract: Second- and third-order finite-difference methods recently applied to problems in high-speed fluid flow are applied to the model advection equation cast in conservative form. The differencing methods considered use forward time differencing with both centered and preferential space differences employed in the predictor-corrector sequences. The free parameter required for stability in the third-order method is adjusted to cause the solution to be either minimum dispersive or minimum dissipative in nature. Results indicate that the third-order method using minimum dispersion is the most accurate method tested. Computer time requirements are approximately twice those needed for second-order techniques.
TL;DR: In this article, the stability and classification of steady-profile plane shocks in liquids are studied by hydrodynamic equations which include the relaxational properties of momentum and heat fluxes, and the thermodynamic behavior during shock deformation is shown to be equivalent to the dissipative motion of a particle described by a generalized Lienard equation.
Abstract: The stability and classification of steady‐profile plane shocks in liquids are studied by hydrodynamic equations which include the relaxational properties of momentum and heat fluxes. The thermodynamic behavior during shock deformation is shown to be equivalent to the dissipative motion of a particle described by a generalized Lienard equation. The stability condition produces relations for the relaxation times for momentum and heat fluxes. These relations are in agreement with acoustic data and other theoretical calculations which produce the relaxation times of 10−13−10−14 sec.
TL;DR: The problem of free energy transfer and transduction in mitochondria is reviewed from the point of view of conservative and dissipative mechanisms to show that conservative transfer is possible within a properly designed medium.
Abstract: The problem of free energy transfer and transduction in mitochondria is reviewed from the point of view of conservative and dissipative mechanisms. Excited states are inherently dissipative and are not considered viable possibilities. If the free energy is already a local minimum and present in the form of potential energy, conservative transfer is possible within a properly designed medium. The design features are compatible with what is known about mitochondria.
TL;DR: In this article, the excitation spectra of a hexagonal lattice of magnetic bubbles is calculated using the methods of lattice dynamics, where the bubbles are allowed one internal zeromode radial degree of freedom and two translational degrees of freedom of the center of mass.
Abstract: The excitation spectra of a hexagonal lattice of magnetic bubbles is calculated using the methods of lattice dynamics. The bubbles are allowed one internal zero‐mode radial degree of freedom and two translational degrees of freedom of the center of mass. This results in three branches of free oscillation, one optical and two acoustical. The equations of motion of the system are obtained from a Lagrangian with a Rayleigh dissipative function. The Fourier transform of these equations yields a secular determinant of order three corresponding to the three branches. The secular equation is a polynomial equation of sixth degree in the complex frequency. This is solved for the directions kx and ky. The interbubble potential is approximated by a dipole‐dipole potential, and restricted to nearest neighbors. The magnetostatic bubble self‐energy is replaced by the analytic approximation of Josephs and Callen. For a close‐packed lattice with no coupling between the radial and translational degrees of freedom, the opt...
01 Jan 1974
TL;DR: An expression for the eikonal approximation for the gravitational radiation absorbed by a dissipative fluid is given in this article, where it is shown that the approximation is eikonormal.
Abstract: An expression is found in the eikonal approximation for the gravitational radiation absorbed by a dissipative fluid.
TL;DR: In this article, a simple flow configuration consisting of the turbulent mixing layer of uniform mean velocity is considered, and the analysis of the laser amplification properties of a turbulent chemically reacting stream consisting of hydrogen, fluorine and the first four vibrational levels of the HF molecules are analyzed.
TL;DR: In this paper, two representations for the current on an isolated antenna in an arbitrary, homogeneous, isotropic medium have been obtained, the polynomial and the trigonometric forms, each with an exponential multiplier.
Abstract: Two representations for the current on an isolated antenna in an arbitrary, homogeneous, isotropic medium have been obtained. These are the polynomial and the trigonometric forms, each with an exponential multiplier. The representations are used for solving coupled integral equations for two antennas in a dissipative medium. Measurements made over a wide range of the parameters of the medium, antenna lengths, and separations (in the case of coupled antennas) indicate a close agreement between the computed and observed values for the admittance and the current and charge distributions for isolated as well as coupled antennas.
01 Jan 1974