Showing papers on "Dissipative system published in 2008"
TL;DR: In this paper, the possibility of using a dissipative process to prepare a quantum system in a desired state was investigated, and for any multipartite pure state, a process for which this state is obtained was derived.
Abstract: We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is ...
598 citations
TL;DR: In this article, a self-centering energy dissipative (SCED) bracing system was proposed for large axial deformations without structural damage while providing stable energy dissipation capacity and a restoring force.
Abstract: Buildings designed according to modern seismic codes are expected to develop a controlled ductile inelastic response during major earthquakes, implying extensive structural damage after a design level earthquake, along with possibly substantial residual deformations. To address this drawback of traditional yielding systems, a new bracing system that can undergo large axial deformations without structural damage while providing stable energy dissipation capacity and a restoring force has recently been developed. The proposed bracing member exhibits a repeatable flag-shaped hysteretic response with full recentering capabilities, therefore eliminating residual deformations. The mechanics of this new system are first explained, the equations governing its design and response are outlined, and one embodiment of the system, which combines a friction dissipative mechanism and Aramid tensioning elements, is further studied. Results from component tests, full-scale (reduced length) quasi-static axial tests, and quasi-static and dynamic seismic tests on a full-scale frame system are presented. Experimental results confirm the expected self-centering behavior of the self-centering energy dissipative (SCED) bracing system within the target design drift. Results also confirm the validity of the design and behavior equations that were developed. It is concluded that the proposed SCED concept can represent a viable alternative to current braced frame systems because of its attractive self-centering property and because the simplicity of the system allows it to be scaled to any desired strength level.
494 citations
TL;DR: In this paper, the cubic-quintic Ginzburg-Landau equation is applied to the normal-dispersion fiber laser to obtain dissipative temporal solitons.
Abstract: Mode-locked fiber lasers in which pulse shaping is based on filtering of a frequency-chirped pulse are analyzed with the cubic-quintic Ginzburg-Landau equation. An exact analytical solution produces a variety of temporal and spectral shapes, which have not been observed in any experimental setting to our knowledge. Experiments agree with the theory over a wide range of parameters. The observed pulses balance gain and loss as well as phase modulations, and thus constitute dissipative temporal solitons. The normal-dispersion fiber laser allows systematic exploration of this class of solitons.
431 citations
01 Jan 2008
TL;DR: In this paper, the authors considered the problem of dissipative dynamical systems in unbounded domains and showed that the dynamics generated by dissipative PDEs in such domains are purely infinite dimensional and do not possess any finite dimensional reduction principle.
Abstract: Publisher Summary The study of the asymptotic behavior of dynamical systems arising from mechanics and physics is a capital issue because it is essential for practical applications to be able to understand and even predict the long time behavior of the solutions of such systems. A dynamical system is a (deterministic) system that evolves with respect to the time. Such a time evolution can be continuous or discrete (i.e., the state of the system is measured only at given times, for example, every hour or every day). The chapter essentially considers continuous dynamical systems. While the theory of attractors for dissipative dynamical systems in bounded domains is rather well understood, the situation is different for systems in unbounded domains and such a theory has only recently been addressed (and is still progressing), starting from the pioneering works of Abergel and Babin and Vishik. The main difficulty in this theory is the fact that, in contrast to the case of bounded domains discussed above, the dynamics generated by dissipative PDEs in unbounded domains is (as a rule) purely infinite dimensional and does not possess any finite dimensional reduction principle. In addition, the additional spatial “unbounded” directions lead to the so-called spatial chaos and the interactions between spatial and temporal chaotic modes generate a space–time chaos, which also has no analogue in finite dimensions.
321 citations
TL;DR: In this article, it was shown that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range, and that the time needed to establish this range is shorter than the eddy-turnover time, and is related to dispersive effects.
Abstract: Magnetic fluctuations in the solar wind are distributed according to Kolmogorov’s power law f −5/3 below the ion cyclotron frequency fci. Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dissipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum ∼ k −7/3+2α , which
278 citations
01 Jan 2008
TL;DR: Three sources and three component parts of the concept of dissipative solitons are discussed in this article.They include: 1) Dissipative Brillouin Solitons in Viscous Flows and 2) Cavity Soliton in Semiconductor Devices.
Abstract: Three Sources and Three Component Parts of the Concept of Dissipative Solitons.- Solitons in Viscous Flows.- Cavity Solitons in Semiconductor Devices.- Dissipative Solitons in Laser Systems with Non-Local and Non-Instantaneous Nonlinearity.- Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities.- Temporal Soliton #x201C Molecules#x201D in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations.- Compounds of Fiber-Optic Solitons.- Dissipative Nonlinear Structures in Fiber Optics.- Three-Wave Dissipative Brillouin Solitons.- Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators.- Discrete Breathers with Dissipation.- Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport.- Coherent Optical Pulse Dynamics in Nano-composite Plasmonic Bragg Gratings.- Collective Focusing and Modulational Instability of Light and Cold Atoms.- On Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles.- Propagation of Traveling Pulses in Cortical Networks.- Wave Phenomena in Neuronal Networks.- Spiral Waves and Dissipative Solitons in Weakly Excitable Media.
274 citations
TL;DR: In this paper, the Parker model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry within the framework of reduced magnetohydrodynamics.
Abstract: The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry within the framework of reduced magnetohydrodynamics. Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled; nevertheless, current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions (~1000 km) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive "bursty" heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine brightly in these wavelengths with little evidence of entangled features. The different regimes of weak and strong magnetohydrodynamic turbulence that develop and their influence on coronal heating scalings are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in stronger loop fields and lead to larger heating rates than in weak field regions.
239 citations
TL;DR: In this article, a fractional reaction-diffusion system with two types of variables: activator and inhibitor, is modeled by cubical nonlinearity and a computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented.
204 citations
TL;DR: In this article, a two-timescale expansion of the Einstein equation for the leading order, adiabatic gravitational waveforms generated by an inspiral is presented. But the authors only consider the case where the self-forces of the inspirals are known.
Abstract: Inspirals of stellar-mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. The detection and analysis of these signals rely on accurate theoretical models of the binary dynamics. We cast the equations describing binary inspiral in the extreme mass ratio limit in terms of action-angle variables, and derive properties of general solutions using a two-timescale expansion. This provides a rigorous derivation of the prescription for computing the leading order orbital motion. As shown by Mino, this leading order or adiabatic motion requires only knowledge of the orbit-averaged, dissipative piece of the self-force. The two-timescale method also gives a framework for calculating the post-adiabatic corrections. For circular and for equatorial orbits, the leading order corrections are suppressed by one power of the mass ratio, and give rise to phase errors of order unity over a complete inspiral through the relativistic regime. These post-1-adiabatic corrections are generated by the fluctuating, dissipative piece of the first order self-force, by the conservative piece of the first order self-force, and by the orbit-averaged, dissipative piece of the second order self-force. We also sketch a two-timescale expansion of the Einstein equation, and deduce an analytic formula for the leading order, adiabatic gravitational waveforms generated by an inspiral.
196 citations
TL;DR: It is shown that the use of a high power alpha of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid conservative dynamics with a finite range of spatial Fourier modes.
Abstract: It is shown that the use of a high power alpha of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid conservative dynamics with a finite range of spatial Fourier modes. Those at large wave numbers thermalize, whereas modes at small wave numbers obey ordinary viscous dynamics [C. Cichowlas et al., Phys. Rev. Lett. 95, 264502 (2005)10.1103/Phys. Rev. Lett. 95.264502]. The energy bottleneck observed for finite alpha may be interpreted as incomplete thermalization. Artifacts arising from models with alpha>1 are discussed.
École normale supérieure de Lyon1, University of Rome Tor Vergata2, Max Planck Society3, University of Twente4, Sapienza University of Rome5, University of Chicago6, Ruhr University Bochum7, National Research Council8, ETH Zurich9, Centre national de la recherche scientifique10, Georgia Institute of Technology11
TL;DR: Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.
Abstract: We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R 2 120:740. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.
TL;DR: A general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes is derived and the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise are studied.
Abstract: We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.
TL;DR: In this paper, the authors present explicit kinetic equations for quantum transport through a general molecular quantum-dot, accounting for all contributions up to 4th order perturbation theory in the tunneling Hamiltonian and the complete molecular density matrix.
Abstract: We present explicit kinetic equations for quantum transport through a general molecular quantum-dot, accounting for all contributions up to 4th order perturbation theory in the tunneling Hamiltonian and the complete molecular density matrix. Such a full treatment describes not only sequential, cotunneling and pair tunneling, but also contains terms contributing to renormalization of the molecular resonances as well as their broadening. Due to the latter all terms in the perturbation expansion are automatically well-defined for any set of system parameters, no divergences occur and no by-hand regularization is required. Additionally we show that, in contrast to 2nd order perturbation theory, in 4th order it is essential to account for quantum coherence between non-degenerate states, entering the theory through the non-diagonal elements of the density matrix. As a first application, we study a single-molecule transistor coupled to a localized vibrational mode (Anderson-Holstein model). We find that cotunneling-assisted sequential tunneling processes involving the vibration give rise to current peaks i.e. negative differential conductance in the Coulomb-blockade regime. Such peaks occur in the cross-over to strong electron-vibration coupling, where inelastic cotunneling competes with Franck-Condon suppressed sequential tunneling, and thereby indicate the strength of the electron-vibration coupling. The peaks depend sensitively on the coupling to a dissipative bath, thus providing also an experimental probe of the Q-factor of the vibrational motion.
TL;DR: In this article, the entire set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal), and the expansion-free condition is integrated.
Abstract: Spherically symmetric expansion-free distributions are systematically studied. The entire set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal), and the expansion-free condition is integrated. In order to understand the physical meaning of expansion-free motion, two different definitions for the radial velocity of a fluid element are discussed. It is shown that the appearance of a cavity is inevitable in the expansion-free evolution. The nondissipative case is considered in detail, and the Skripkin model is recovered.
TL;DR: In this paper, the authors prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary, without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function.
Abstract: The linear viscoelastic equation is considered. We prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary, without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function. Our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity. The proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates.
TL;DR: In this paper, the authors proposed an interferometry-by-deconvolution approach which replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications.
Abstract: Seismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry‐by‐deconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlled‐source electromagnetic (CSEM) data. Interferometry‐by‐deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.
TL;DR: In this paper, the authors explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field, which requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit.
Abstract: We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in [1].
TL;DR: The recent resurgence in interest in dissipative solitons has led to significant advances in our understanding of the origin and properties of these states, and these in turn suggest new questions, both general and system-specific.
Abstract: Stationary spatially localized structures, sometimes called dissipative solitons, arise in many interesting and important applications, including buckling of slender structures under compression, nonlinear optics, fluid flow, surface catalysis, neurobiology and many more. The recent resurgence in interest in these structures has led to significant advances in our understanding of the origin and properties of these states, and these in turn suggest new questions, both general and system-specific. This paper surveys these results focusing on open problems, both mathematical and computational, as well as on new applications.
TL;DR: To reduce spurious modes on very distorted meshes, the addition of dissipative terms as penalization in the numerical scheme is studied and compared on examples and a multi-class local time-stepping strategy is presented.
TL;DR: In this paper, the authors studied the physical phenomena involved in the transition between ordinary fluidity concrete and high fluidity concretes according to the aggregate content of the mixture and showed that there exists a strong transition in the rheological behavior of concrete between a regime dominated by the friction between aggregate particles and a regime dominating by hydrodynamic interactions far less dissipative.
TL;DR: In this paper, the decay property of the dissipative Timoshenko system in the one-dimensional whole space is studied and the decay structure is of the regularity-loss type.
Abstract: We study the decay property of the dissipative Timoshenko system in the one-dimensional whole space. We derive the L2 decay estimates of solutions in a general situation and observe that this decay structure is of the regularity-loss type. Also, we give a refinement of these decay estimates for some special initial data. Moreover, under enough regularity assumption on the initial data, we show that the solution approaches the linear diffusion wave expressed in terms of the heat kernels as time tends to infinity. The proof is based on the detailed pointwise estimates of solutions in the Fourier space.
TL;DR: In this paper, the standard and non-standard Lagrangians for dynamical systems with first-order time derivative terms of even and odd powers, and coefficients varying either in time or in space are presented and used to identify classes of equations of motion that admit a Lagrangian description.
Abstract: Dynamical systems described by equations of motion with the first-order time derivative (dissipative) terms of even and odd powers, and coefficients varying either in time or in space, are considered. Methods to obtain standard and non-standard Lagrangians are presented and used to identify classes of equations of motion that admit a Lagrangian description. It is shown that there are two general classes of equations that have standard Lagrangians and one special class of equations that can only be derived from non-standard Lagrangians. In addition, each general class has a subset of equations with non-standard Lagrangians. Conditions required for the existence of standard and non-standard Lagrangians are derived and a relationship between these two types of Lagrangians is introduced. By obtaining Lagrangians for several dynamical systems and some basic equations of mathematical physics, it is demonstrated that the presented methods can be applied to a broad range of physical problems.
TL;DR: In this article, the authors explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field, which requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit.
Abstract: We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.3459.
TL;DR: A reformulation of the refined similarity hypothesis in terms of the mass-weighted velocity rho1/3v yields scaling laws that are almost insensitive to the forcing of supersonic turbulent flow, implying that the most intermittent dissipative structures are shocks closely following the scaling of Burgers turbulence.
Abstract: The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i.e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of supersonic turbulent flow driven by external forcing, we demonstrate that this is not generally true for the two-point velocity statistics of compressible turbulence. However, a reformulation of the refined similarity hypothesis in terms of the mass-weighted velocity rho1/3v yields scaling laws that are almost insensitive to the forcing. The results imply that the most intermittent dissipative structures are shocks closely following the scaling of Burgers turbulence.
TL;DR: The attention is focused on the design of linear state feedback controllers and impulsive controllers such that, for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators, the stochastic hybrid system is stochastically robustly stable and strictly ( Q, S, R ) -dissipative.
Book•
21 Aug 2008
TL;DR: In this paper, a case study of chaos in distributed systems is presented, where forced and coupled chemical oscillators are used to simulate chaotic dynamics in a distributed system with parametric dependences, bifurcations and chaos.
Abstract: Introduction 1 Differential equations, maps and asymptotic behaviour 2 Transition from order to chaos 3 Numerical methods for studies of parametric dependences, bifurcations and chaos 4 Chaotic dynamics in experiments 5 Forced and coupled chemical oscillators: a case study of chaos 6 Chaos in distributed systems Appendices Bibliography Index
TL;DR: In this article, the stability and causality of the Landau-Lifshitz theory and the Israel-Stewart-type causal dissipative hydrodynamics are discussed.
Abstract: The stability and causality of the Landau–Lifshitz theory and the Israel–Stewart-type causal dissipative hydrodynamics are discussed. We show that the problems of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.
TL;DR: In this paper, the stability threshold of a natural circulation loop with supercritical fluid is not confined to the near-peak region of the (steady state) flow-power curve.