Showing papers on "Dissipative system published in 1998"

Dissipative heating and hurricane intensity

Abstract: Dissipative heating has not been accounted for in either numerical simulations of hurricanes or in theories for the maximum intensity of hurricanes. We argue that the bulk of dissipative heating occurs in the atmospheric boundary layer near the radius of maximum winds and, using both theory and numerical simulation, show that dissipative heating increases maximum wind speeds in tropical cyclones by about 20%.

An action for black hole membranes

Abstract: The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipative equations. Using a Euclidean path integral, we show that familiar semi-classical thermodynamic properties of black holes also emerge from the membrane action. Finally, in a Hamiltonian description, we establish the validity of a minimum entropy production principle for black holes.

Strong dissipative behavior in quantum field theory

Abstract: We study the conditions under which an overdamped regime can be attained in the dynamic evolution of a quantum field configuration. Using a real-time formulation of finite temperature field theory, we compute the effective evolution equation of a scalar field configuration, quadratically interacting with a given set of other scalar fields. We then show that, in the overdamped regime, the dissipative kernel in the field equation of motion is closely related to the shear viscosity coefficient, as computed in scalar field theory at finite temperature. The effective dynamics is equivalent to a time-dependent Ginzburg-Landau description of the approach to equilibrium in phenomenological theories of phase transitions. Applications of our results, including a recently proposed inflationary scenario called ``warm inflation,'' are discussed.

Fluid particle model

Abstract: We present a mechanistic model for a Newtonian fluid called fluid particle hydrodynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose a heuristic derivation of a dissipative particle dynamics algorithm that incorporates shear forces between dissipative particles. The inclusion of these noncentral shear forces requires the consideration of angular velocities of the dissipative particles in order to comply with the conservation of angular momentum. It is shown that the equilibrium statistical mechanics requirement that the linear and angular velocity fields are Gaussian is sufficient to construct the random thermal forces between dissipative particles. The proposed algorithm is very similar in structure to the (isothermal) smoothed particle hydrodynamics algorithm. In this way, this work represents a generalization of smoothed particle hydrodynamics that incorporates consistently thermal fluctuations and exact angular momentum conservation. It contains also the dissipative particle dynamics algorithm as a special case. Finally, the kinetic theory of the dissipative particles is derived and explicit expressions for the transport coefficients of the fluid in terms of model parameters are obtained. This allows us to discuss resolution issues for the model.

An anisotropic model of damage and frictional sliding for brittle materials

Abstract: The paper provides important developments for the model of anisotropic damage by mesocrack growth, accounting for unilateral behaviour relative to crack closure (Dragon and Halm, 1996, Halm and Dragon, 1996). Frictional sliding of closed microcrack systems is introduced here as an additional dissipative mechanism, which is considered to be coupled with the primary dissipative mechanism (damage by microcrack growth). Indeed, accounting for frictional sliding completes the description of moduli recovery in the existing model by adding to the normal moduli recovery effect (normal with respect to the crack plane) the substantial recovery of shear moduli. In parallel to damage modelling, the internal variable related to frictional sliding is a second-order tensor. Even if the unilateral effect and friction incipience are characterized by a discontinuity of effective moduli, it is crucial to ensure continuity of the energy and stress-response. Relevant conditions are proposed to ensure this. As far as frictional sliding is concerned, and unlike most of the models based on the classical Coulomb law, the corresponding criterion is given here in the space of thermodynamic forces representing a form of energy release with respect to the sliding internal variable. It appears that the normality rule in the latter space for sliding evolution is not physically contradictory with the observed phenomenon. The pertinence of the proposed theory, relative to the maximum dissipation hypothesis for both mechanisms, is illustrated by simulating loading paths involving damage and friction effects.

Diffusive representation of pseudo-differential time-operators

Abstract: The concept of ''diffusive representation'' was previously introduced in the aim of transforming non standard convolutive causal operators such as fractional integrodifferential ones, into infinite-dimension dissipative classical input-output dynamic systems. The existence of an explicit dissipative semigroup makes then possible the use of classical tools of functional and numerical analysis of PDE, energy methods, control, filtering, etc., generally ill-fitted to the standard convolutive formulations, namely when long memory dynamics are present. The aim of the paper is to present in a synthetic statement, first the general frame of diffusive representations, and secondly some of the essential characteristics and properties of this new tool. Simple and concrete examples are given. More significant applications (essentially in the fractional context) will be found in the referenced papers.

On tide propagation in convergent estuaries

Abstract: We revisit the problem of one-dimensional tide propagation in convergent estuaries considering four limiting cases defined by the relative intensity of dissipation versus local inertia in the momentum equation and by the role of channel convergence in the mass balance. In weakly dissipative estuaries, tide propagation is essentially a weakly nonlinear phenomenon where overtides are generated in a cascade process such that higher harmonics have increasingly smaller amplitudes. Furthermore, nonlinearity gives rise to a seaward directed residual current. As channel convergence increases, the distortion of the tidal wave is enhanced and both tidal wave speed and wave lenght increase. The solution loses its wavy character when the estuary reaches its “critical convergence”; above such convergence the weakly dissipative limit becomes meaningless. Finally, when channel convergence is strong or moderate, weakly dissipative estuaries turn out to be ebb dominated. In strongly dissipative estuaries, tide propagation becomes a strongly nonlinear phenomenon that displays peaking and sharp distortion of the current profile, and that invariably leads to flood dominance. As the role of channel convergence is increasingly counteracted by the diffusive effect of spatial variations of the current velocity on flow continuity, tidal amplitude experiences a progressively decreasing amplification while tidal wave speed increases. We develop a nonlinear parabolic approximation of the full de Saint Venant equations able to describe this behaviour. Finally, strongly convergent and moderately dissipative estuaries enhance wave peaking as the effect of local inertia is increased. The full de Saint Venant equations are the appropriate model to treat this case.

On the characteristics of vortex filaments in isotropic turbulence

Abstract: The statistical properties of the strong coherent vortices observed in numerical simulations of isotropic turbulence are studied. When compiled at axial vorticity levels ω/ω′∼Re1/2λ, where ω′ is the r.m.s. vorticity magnitude for the flow as a whole, they have radii of the order of the Kolmogorov scale and internal velocity differences of the order of the r.m.s. velocity of the flow u′. Theoretical arguments are given to explain these scalings. It is shown that the filaments are inhomogeneous Burgers' vortices driven by an axial stretching which behaves like the strain fluctuations of the background flow. It is suggested that they are the strongest members in a class of coherent objects, the weakest of which have radii of the order of the Taylor microscale, and indirect evidence is presented that they are unstable. A model is proposed in which this instability leads to a cascade of coherent filaments whose radii are below the dissipative scale of the flow as a whole. A family of such cascades separates the self-similar inertial range from the dissipative limit. At the vorticity level given above, the filaments occupy a volume fraction which scales as Re−2λ, and their total length increases as O(Reλ). The length of individual filaments scales as the integral length of the flow, but there is a shorter internal length of the order of the Taylor microscale.

Moving glass theory of driven lattices with disorder

Abstract: We study periodic structures, such as vortex lattices, moving in a random pinning potential under the action of an external driving force. As predicted in T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 76, 3408 (1996) the periodicity in the direction transverse to motion leads to a different class of driven systems: the moving glasses. We analyze using several renormalization-group techniques, the physical properties of such systems both at zero and nonzero temperature. The moving glass has the following generic properties (in $dl~3$ for uncorrelated disorder) (i) decay of translational long-range order, (ii) particles flow along static channels, (iii) the channel pattern is highly correlated along the direction transverse to motion through elastic compression modes, (iv) there are barriers to transverse motion. We demonstrate the existence of the transverse critical force at $T=0$ and study the transverse depinning. A ``static random force'' both in longitudinal and transverse directions is shown to be generated by motion. Displacements are found to grow logarithmically at large scale in $d=3$ and as a power law in $d=2.$ The persistence of quasi-long-range translational order in $d=3$ at weak disorder, or large velocity leads to the prediction of the topologically ordered moving Bragg glass. This dynamical phase which is a continuation of the static Bragg glass studied previously, is shown to be stable to a nonzero temperature. At finite but low temperature, the channels broaden and survive and strong nonlinear effects still exist in the transverse response, though the asymptotic behavior is found to be linear. In $d=2,$ or in $d=3$ at intermediate disorder, another moving glass state exists, which retains smectic order in the transverse direction: the moving transverse glass. It is described by the moving glass equation introduced in our previous work. The existence of channels allows us to naturally describe the transition towards plastic flow. We propose a phase diagram in temperature, force, and disorder for the static and moving structures. For correlated disorder we predict a ``moving Bose glass'' state with anisotropic transverse Meissner effect, localization, and transverse pinning. We discuss the effect of additional linear and nonlinear terms generated at large scale in the equation of motion. Generalizations of the moving glass equation to a larger class of nonpotential glassy systems described by zero temperature and nonzero temperature disordered fixed points (dissipative glasses) are proposed. We discuss experimental consequences for several systems, such as the anomalous Hall effect in the Wigner crystal, transverse critical current in the vortex lattice, and solid friction.

Droplet Spreading: Partial Wetting Regime Revisited

Abstract: We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a non-equilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of mechanical dissipative systems, in which the driving force, i.e. the gradient of the system's Lagrangian function, is balanced against the rate of the dissipation function. In our case the driving force is the loss of the droplet's free energy due to the increase of its base radius, while the dissipation occurs due to viscous flows in the core of the droplet and due to frictional processes in the vicinity of the advancing contact line, associated with attachment of fluid particles to solid. Within this approach we derive closed-form equations for the evolution of the droplet's base radius, and specify several regimes at which different dissipation channels dominate. Our analytical predictions compare very well with experimental data.

Theory of the magnetic damping constant

Abstract: The aim of this paper is to express the effects of basic dissipative mechanisms involved in the dynamics of the magnetization field in terms of the one most commonly observed quantity: the spatial average of that field. The mechanisms may be roughly divided into direct relaxation to the lattice, and indirect relaxation via excitation of many magnetic modes. Two illustrative examples of these categories are treated; direct relaxation via magnetostriction into a lattice of known elastic constant, and relaxation into synchronous spin waves brought about by imperfections. Finally, a somewhat speculative account is presented of time constants to be expected in magnetization reversal.

Quantum Dissipative Dynamics: A Numerically Exact Methodology

Abstract: A fully quantum mechanical methodology for simulating the time evolution of low-dimensional systems in harmonic dissipative environments is presented. The key features of the method are the numeric...

Dissipative particle dynamics

Abstract: Dissipative particle dynamics is a relatively new simulation method in the colloid and interface science field. Recent applications include simulations of the dynamics and rheology of polymers in solution, the dynamics of microphase separation in block copolymer melts, and the effects of hydrodynamics in spinodal decomposition.

Driving, conservation, and absorbing states in sandpiles

Abstract: We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension $d_c=4$. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.

Quasilinear Hyperbolic Systems and Dissipative Mechanisms

Abstract: Frictional damping globally defined classical solutions and their nonlinear diffusive phenomena frictional damping - globally defined weak solutions and their nonlinear diffusive phenomena relaxation the influence of the dissipation mechanism on the qualitative behaviour of solutions viscosity vanishing and nonlinear stability of waves.

Statistical Properties of Magnetic Activity in the Solar Corona

Abstract: The long-time statistical behavior of a two-dimensional section of a coronal loop subject to random magnetic forcing is presented. The highly intermittent nature of dissipation is revealed by means of magnetohydrodynamic (MHD) turbulence numerical simulations. Even with a moderate magnetic Reynolds number, intermittency is clearly present in both space and time. The response of the loop to the random forcing, as described either by the time series of the average and maximum energy dissipation or by its spatial distribution at a given time, displays a Gaussian noise component that may be subtracted to define discrete dissipative events. Distribution functions of both maximum and average current dissipation, for the total energy content, the peak activity, and the duration of such events are all shown to display robust scaling laws, with scaling indices δ that vary from δ -1.3 to δ -2.8 for the temporal distribution functions, while δ -2.6 for the overall spatial distribution of dissipative events.

Homogeneous cooling of rough, dissipative particles : Theory and simulations

Abstract: We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event-driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times [Formula Presented] translational and rotational energy are found to change linearly with [Formula Presented] For large times both energies decay like [Formula Presented] with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e., density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.

Dynamical simulation of current fluctuations in a dissipative two-state system

Abstract: Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over the real-time paths under the influence of colored noise. The nature of the transition from coherent to incoherent dynamics at low temperatures is re-examined.

Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas

Abstract: The relaxation theory of a two-species magnetofluid is presented. This generalizes the familiar magnetohydrodynamic (single-fluid) theory. The two-fluid invariants are the self-helicities, one for each species. Their “local” invariance follows from the helicity transport equations, which are derived. The global forms of the self-helicities are examined in a weakly dissipative system. They are shown to pass three tests of ruggedness (“relative” invariance compared with the magnetofluid energy): the cascade test; the selective decay test; and the stability to resistive modes test. Once ruggedness is established, relaxed states can be found by minimizing the magnetofluid energy subject to constrained self-helicities. The Euler equations are found by a variational procedure. Example equilibria are presented that resemble field-reversed configurations (FRCs) and tokamaks. These states are characterized by finite pressure and significant sheared flows. Throughout the analysis it is shown how this more general theory reduces to the magnetohydrodynamic (single-fluid) theory for suitable reducing assumptions.

Robust dissipative control for linear systems with dissipative uncertainty

Abstract: This paper focuses on the problem of quadratic dissipative control for linear systems with or without uncertainty We consider the design of feedback controllers to achieve (robust) asymptotic stability and strict quadratic dissipativeness Both linear static state feedback and dynamic output feedback controllers are considered First, the equivalence between strict quadratic dissipativeness of linear systems and a H performance is established Necessary and sufficient conditions for the solution of the quadratic dissipative control problem are then obtained using a linear matrix inequality (LMI) approach As for uncertain systems, we consider structured uncertainty characterized by a dissipative system This uncertainty description is quite general and contains commonly used types of uncertainty, such as norm-bounded and positive real uncertainties, as special cases It is shown that the robust dissipative control problem can be solved in terms of a scaled quadratic dissipative control problem without un

Exponential stability of a thermoelastic system with free boundary conditions without mechanical dissipation

Abstract: We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. Lagnese, Boundary Stabilization of Thin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case---where rotational forces are neglected---in [Z. Liu and S. Z. Heng, Quarterly Appl. Math., 55 (1997), pp. 551-564]). The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate a fortiori the desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for related work. Moreover, the particular choice of our multiplier becomes clear only after recasting the PDE model into an associated abstract evolution equation.

A variational approach of nonlinear dissipative pulse propagation

Abstract: A variational technique to deal with nonlinear dissipative pulse propagation is established. By means of a generalization of the Kantorovitch method, suitable for non-conservative systems, we are able to cope with an extended nonlinear Schrodinger equation (NLSE) which describes pulse propagation under the influence of nonlinear loss and/or gain, in particular, in the presence of two-photon absorption (TPA). Based on the characteristics of the exact solution of the NLSE in the absence of TPA, we investigate the effects of frequency dispersion of the nonlinear susceptibility associated to the two-photon resonance, obtaining the necessary conditions for a solitary wave solution, even in the presence of a self-steepening term.

Reduced models in the medium frequency range for general dissipative structural-dynamics systems

Abstract: This paper presents a theoretical approach for constructing a reduced model in the medium-frequency range in the area of structural dynamics for a general three-dimensional anisotropic and inhomogeneous viscoelastic bounded medium. All the results presented can be used for beams, plates and shells. The boundary value problem in the frequency domain and its variational formulation are presented. For a given medium-frequency band, an energy operator which is intrinsic to the dynamical system is introduced and mathematically studied. This energy operator depends on the dissipative part of the dynamical system. It is proved that this operator is a positive-definite symmetric trace operator in a Hilbert space and that its dominant eigensubspace allows a reduced model to be constructed using the Ritz-Galerkin method. An effective construction of the dominant subspace using the subspace iteration method is developed. Finally, an example is given to validate the concepts and the algorithms.