Showing papers on "Dissipative system published in 1992"
TL;DR: An alternative approach using a wave-function treatment to describe the atomic system and it is shown that this treatment is equivalent to the standard density matrix approach leading to the OBE's.
Abstract: A novel treatment of dissipation of energy from a ``small'' quantum system to a reservoir is presented. We replace the usual master equation for the small-system density matrix by a wave-function evolution including a stochastic element. This wave-function approach provides new insight and it allows calculations on problems which would otherwise be exceedingly complicated. The approach is applied here to a two- or three-level atom coupled to a laser field and to the vacuum modes of the quantized electromagnetic field.
1,532 citations
TL;DR: In this paper, the authors describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter.
401 citations
TL;DR: In this paper, the authors investigated the modulational instability in a synchronously pumped nonlinear dispersive ring cavity and derived the formation of stable temporal dissipative structures for both the normal and anomalous dispersion regime of the fiber.
333 citations
01 Jan 1992
TL;DR: In this article, a volume devoted to stochastic and chaotic oscillations in dissipative systems is presented, which deals with mathematical models of deterministic, discrete and distributed dynamical systems.
Abstract: This volume is devoted to stochastic and chaotic oscillations in dissipative systems. It first deals with mathematical models of deterministic, discrete and distributed dynamical systems. It then considers the two basic trends of order and chaos, and describes stochasticity transformers, amplifiers and generators, turbulence and phase portraits of steady-state motions and their bifurcations. The books also treats the topics of stochastic and chaotic attractors, as well as the routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, in a chapter which comprises more than one-third of the book, examples are presented of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems.
249 citations
TL;DR: In this paper, it was shown that the modulation equation dominates the dynamics of the full problem locally, at least over a long time-scale, for systems with no quadratic interaction term.
Abstract: Modulation equations play an essential role in the understanding of complicated systems near the threshold of instability. Here we show that the modulation equation dominates the dynamics of the full problem locally, at least over a long time-scale. For systems with no quadratic interaction term, we develop a method which is much simpler than previous ones. It involves a careful bookkeeping of errors and an estimate of Gronwall type.As an example for the dissipative case, we find that the Ginzburg–Landau equation is the modulation equation for the Swift–Hohenberg problem. Moreover, the method also enables us to handle hyperbolic problems: the nonlinear Schrodinger equation is shown to describe the modulation of wave packets in the Sine–Gordon equation.
220 citations
TL;DR: A damped hyerbolic equation with critical exponent was proposed in this paper, where the critical exponent is defined as the number of elements in a damped hyperbolic equation. Communications in Partial Differential Equations: Vol 17, No. 5-6, pp. 841-866.
Abstract: (1992). A damped hyerbolic equation with critical exponent. Communications in Partial Differential Equations: Vol. 17, No. 5-6, pp. 841-866.
192 citations
TL;DR: In this article, the authors compared the geometrothermodynamic effects of the bulk viscosity and matter creation dissipative mechanisms in the context of the FRW metric.
162 citations
TL;DR: In this paper, it is shown that a new type of instability of a light field in a dissipative medium (spatiotemporal instability) can be observed by controlling the spatial scale and the topology of the transverse interactions of light fields in a medium with cubic nonlinearity.
Abstract: It is shown that a new type of instability of a light field in a dissipative medium (spatiotemporal instability, which causes the generation of new types of nonlinear light wave) can be observed by controlling the spatial scale and the topology of the transverse interactions of light fields in a medium with cubic nonlinearity. The excitation conditions for optical reverberators, rotating helical waves, and various dissipative structures are experimentally determined. Transformations and interactions of the structures lead to optical turbulence in both space and time. Physical interpretation of these phenomena is based on the parabolic equation for the nonlinear phase shift. It is found that this theoretical model allows one not only to obtain the excitation conditions but to investigate thoroughly such phenomena as hysteresis and nonlinear interactions of structures.
141 citations
TL;DR: In applying the formalism of dissipative dynamical process to ferrofluids, a calculation of the energy of a two-dimensional dipolar domain as a functional of the shape of its boundary is presented.
Abstract: A theory is developed for the dynamics of pattern formation in quasi-two-dimensional domains of magnetic fluids (ferrofluids) in transverse magnetic fields. The pattern formation is treated as a dissipative dynamical process, with the motion derived variationally from a static energy functional using minimal assumptions. This dynamics is one instance of a general formalism applicable to any system that can be modeled as a closed curve in a plane. In applying the formalism to ferrofluids, we present a calculation of the energy of a two-dimensional dipolar domain as a functional of the shape of its boundary. A detailed linear stability analysis of nearly circular shapes is presented, and pattern formation in the nonlinear regime, far from the onset of instability, is studied by numerical solution of the nonlinear, nonlocal evolution equations. The highly branched patterns obtained numerically bear a qualitative resemblance to those found experimentally. The time evolution exhibits sensitive dependence on initial conditions, suggesting the existence of many local minima in the space of accessible shapes. The analysis also provides a deterministic starting point for a theory of pattern formation in dipolar monolayers at the air-water interface, in which thermal fluctuations play a more dominant role.
123 citations
TL;DR: In this article, a nonlinear stabilizing feedback control law together with an observer is used to stabilize a class of bilinear systems using an observer, and it can be proved that the result is a globally asymptotically stable system.
Abstract: Input-output stabilization of a class of bilinear systems using a nonlinear stabilizing feedback control law together with an observer, is studied In some cases, it can be proved that the result is a globally asymptotically stable system >
108 citations
TL;DR: The general formalism of Langer is applied to compute the nucleation rate for systems of relativistic particles with a zero or small baryon-number density and which undergo first-order phase transitions and an expression for the pre-exponential factor is obtained.
Abstract: We apply the general formalism of Langer to compute the nucleation rate for systems of relativistic particles with a zero or small baryon-number density and which undergo first-order phase transitions. In particular, we obtain an expression for the pre-exponential factor and it is proportional to the viscosity. The initial growth rate of a critical size bubble or droplet is limited by the ability of dissipative processes to transport latent heat away from the surface.
TL;DR: In this article, a mathematical and numerical framework has been worked out to represent the density operator in phase space and to propagate it in time under dissipative conditions, based on the Fourier pseudospectral method which allows a description both in configuration as well as in momentum space.
Abstract: A mathematical and numerical framework has been worked out to represent the density operator in phase space and to propagate it in time under dissipative conditions. The representation of the density operator is based on the Fourier pseudospectral method which allows a description both in configuration as well as in momentum space. A new propagation scheme which treats the complex eigenvalue structure of the dissipative Liouville superoperator has been developed. The framework has been designed to incorporate modern computer architecture such as parallelism and vectorization. Comparing the results to closed-form solutions exponentially fast convergence characteristics in phase space as well as in the time propagation is demonstrated. As an example of its usefulness, the new method has been successfully applied to dissipation under the constraint of selection rules. More specifically, a harmonic oscillator which relaxes to equilibrium under the constraint of second-order coupling to the bath was studied.
TL;DR: In this paper, a reconsideration of the fundamental role of the characteristics in the determination of the up-wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov-Galerkin scheme entitled the characteristic dissipative Galerkin method.
Abstract: Many open‐channel flow problems may be modeled as depth‐averaged flows. Petrov‐Galerkin finite element methods, in which up‐wind weighted test functions are used to introduce selective numerical dissipation, have been used successfully for modeling open‐channel flow problems. The underlying consistency and generality of the finite element method is attractive because separate computational algorithms for subcritical and supercritical flow are not required and algorithm extension to the two‐dimensional depth‐averaged flow equations is straightforward. Here, a reconsideration of the fundamental role of the characteristics in the determination of the up‐wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov‐Galerkin scheme entitled the characteristic dissipative Galerkin method. A linear stability analysis illustrates the selective damping of short wavelengths and excellent phase accuracy achieved by this scheme, as well as its insensitivity to parameter variati...
TL;DR: In this paper, the authors consider the evolution of a two-level system driven by a nonself-adjoint Hamiltonian H( in t) and treat the adiabatic limit in to 0.
Abstract: The authors consider the evolution of a two-level system driven by a nonself-adjoint Hamiltonian H( in t) and treat the adiabatic limit in to 0. While adiabatic theorem-like results do not hold true in general for this case, they prove that they are still valid for the subspace corresponding to the eigenvalue having the largest imaginary part (least dissipative eigenvalue). The theory gives the full asymptotic expansion of the evolution restricted to this subspace. The first correction beyond Berry's phase is to their best knowledge given explicitly for the first time.
TL;DR: In this article, results of experimental, analytical and computer studies concerning bifurcations on the boundaries of the synchronization regime of chaotic self-oscillations are provided concerning two dissipative coupled electronic circuits with possible chaotic dynamics.
Abstract: In a case of two dissipative coupled electronic circuits with possible chaotic dynamics, results of experimental, analytical and computer studies are provided concerning bifurcations on the boundaries of the synchronization regime of chaotic self-oscillations.
TL;DR: In this paper, an explicit solution for the optimal planar dividing surface for multidimensional dissipative systems whose equations of motion are given in terms of coupled generalized Langevin equations is provided.
Abstract: The variational transition state theory approach for dissipative systems is extended in a new direction. An explicit solution is provided for the optimal planar dividing surface for multidimensional dissipative systems whose equations of motion are given in terms of coupled generalized Langevin equations. In addition to the usual dependence on friction, the optimal planar dividing surface is temperature dependent. This temperature dependence leads to a temperature dependent barrier frequency whose zero temperature limit in the one dimensional case is just the usual Kramers–Grote–Hynes reactive frequency. In this way, the Kramers–Grote–Hynes equation for the barrier frequency is generalized to include the effect of nonlinearities in the system potential. Consideration of the optimal planar dividing surface leads to a unified treatment of a variety of problems. These are (a) extension of the Kramers–Grote–Hynes theory for the transmission coefficient to include finite barrier heights, (b) generalization of Langer’s theory for multidimensional systems to include both memory friction and finite barrier height corrections, (c) Langer’s equation for the reactive frequency in the multidimensional case is generalized to include the dependence on friction and the nonlinearity of the multidimensional potential, (d) derivation of the non‐Kramers limit for the transmission coefficient in the case of anisotropic friction, (e) the generalized theory allows for the possibility of a shift of the optimal planar dividing surface away from the saddle point, this shift is friction and temperature dependent, (f) a perturbative solution of the generalized equations is presented for the one and two dimensional cases and applied to cubic and quartic potentials.
TL;DR: These results suggest that microtubular dissipative structures may play an important role both in morphogenesis and in accounting for the sensitivity of biological systems to weak fields and provide another explanation for biological gravitropism.
Abstract: Reduction-diffusion theories can account for both morphogenesis and the sensitivity of biological systems to weak fields. They predict that gravity can cause the symmetry breaking that is necessary for pattern formation. Microtubules play an important role in organizing the cell, and recent studies hae shown that they can form in vitro dissipative structures. We have found that these structures show patterns of microtubular orientation that are gravity dependent and that the gravitational field causes symmetry breaking. This behavior, which cannot be explained by convection, is in accordance with the theory of dissipative structures. These results suggest that microtubular dissipative structures may play an important role both in morphogenesis and in accounting for the sensitivity of biological systems to weak fields. They aso provide another explanation for biological gravitropism.
TL;DR: In this paper, the authors investigate the behavior of a continuum model designed to provide insight into the dynamical development of microstructures observed during displacive phase transformations in certain materials.
Abstract: We investigate the behavior of a continuum model designed to provide insight into the dynamical development of microstructures observed during displacive phase transformations in certain materials. The model is presented within the framework of nonlinear viscoelasticity and is also of interest as an example of a strongly dissipative infinite-dimensional dynamical system whose forward orbits need not lie on a finite-dimensional attracting set, and which can display a subtle dependence on initial conditions quite different from that of classical finite-dimensional “chaos”. We study the problem of dynamical (two-dimensional) anti-plane shear with linear viscoelastic damping. Within the framework of nonlinear hyperelasticity, we consider both isotropic and anisotropic constitutive laws which can allow different phases and we characterize their ability to deliver minimizers and minimizing sequences of the stored elastic energy (Theorem 2.3). Using a transformation due to Rybka, we recast the problem as a semilinear degenerate parabolic system, thereby allowing the application of semigroup theory to establish existence, uniqueness and regularity of solutions in L
p
spaces (Theorem 3.1). We also discuss the issues of energy minimization and propagation of strain discontinuities. We comment on the difficulties encountered in trying to exploit the geometrical properties of specific constitutive laws. In particular, we are unable to obtain analogues of the absence of minimizers and of the non-propagation of strain discontinuities found by Ball, Holmes, James, Pego & Swart [1991] for a one-dimensional model problem. Several numerical experiments are presented, which prompt the following conclusions. It appears that the absence of an absolute minimizer may prevent energy minimization, thereby providing a dynamical mechanism to limit the fineness of observed microstructure, as has been proved in the one-dimensional case. Similarly, viscoelastic damping appears to prevent the propagation of strain discontinuities. During the extremely slow development of fine structure, solutions are observed to display local refinement in an effort to overcome incompatibility with boundary and initial conditions, with the distribution and shape of the resulting finer scales displaying a subtle dependence on initial conditions.
TL;DR: In this article, a hamiltonian amplitude equation, iψ x +ψ tt +2σ|ψ| 2 ψ-∈ψ xt =0 σ=± 1, ∈<<1, is introduced.
Abstract: A new hamiltonian amplitude equation, iψ x +ψ tt +2σ|ψ| 2 ψ-∈ψ xt =0 σ=±1, ∈<<1, is introduced. The equation governs certain instabilities of modulated wave-trains, and the addition of the term -∈ψ xt overcomes the ill-posedness of the unstable nonlinear Schrodinger equation. This new equation is apparently not integrable, but it is a Hamiltonian analogue of the Kuramoto-Sivashinsky equation, which arises in dissipative systems
TL;DR: In this paper, it was proved that certain smooth, global solutions of a class of quasi-linear, dissipative wave equations have precisely the same leading order, long-time, asymptotic behavior as the solutio...
Abstract: It is proved herein that certain smooth, global solutions of a class of quasi-linear, dissipative wave equations have precisely the same leading order, long-time, asymptotic behavior as the solutio...
TL;DR: In this paper, the authors studied the dissipative quantum mechanics of the Hofstadter model and showed that there are an infinite number of phase transition lines whose density grows without limit as the dissipation goes to zero.
TL;DR: In this paper, a multi-dimensional Langevin approach to nuclear dissipative phenomena is presented, without any approximations for the study of induced fission dynamics, and the transient time of the symmetric fission of 213At is calculated and discussed in comparison with empirically deduced value.
TL;DR: In this paper, an SU(1, 1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems, which is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron-phonon system.
Abstract: An SU(1,1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems. The Liouville space formulation, thermo field dynamics, and the disentanglement theorem of SU(1,1) Lie algebra play essential roles in this formulation. In the Liouville space, the time‐evolution equation for the state vector of a system is solved algebraically by using the decomposition formulas of SU(1,1) Lie algebra and the thermal state condition of thermo field dynamics. The presented formulation is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron–phonon system. This algebraic formulation gives a systematic treatment for investigating the phenomena in quantum optical systems.
TL;DR: In this article, the tridimensional pattern selection problem for reaction-diffusion systems was studied analytically and numerically, and the results were validated with the recent experimental results.
01 Jan 1992
TL;DR: In this paper, two interwoven strands describe selected experimental studies of friction carried out by the author over the last 55 years and indicate some of the rather more general ideas that emerged from that work.
Abstract: This paper consists of two interwoven strands. One strand describes selected experimental studies of friction carried out by the author over the last 55 years and indicates some of the rather more general ideas that emerged from that work.
TL;DR: In this article, the authors used numerical flow simulations to study the effect of coherent structures on transport in the context of a two-field, two-dimensional model of dissipative drift-wave turbulence.
Abstract: Numerical flow simulations are used to study the effect of coherent structures on transport in the context of a two‐field, two‐dimensional model of dissipative drift‐wave turbulence. The presence and nature of structures are found to depend on the adiabaticity parameter α=k∥2 VT2/2νeiωs which controls the degree to which the electrons respond to parallel electric fields. Transport estimates based on quasilinear and mixing‐length models are compared with the simulations. In the regime with long‐lived coherent structures, the turbulent particle transport predicted by a standard quasilinear or mean‐field estimate is found to exceed that actually observed in the presence of coherent structures.
TL;DR: In this paper, a survey of quantum and classical Bell-type inequalities, with emphasis on dissipation, spontaneous reduction models, and experimental tests of the universal validity of the quantum theory is presented.
Abstract: Instead of the usual asymptotic passage from quantum mechanics to classical mechanics when a parameter tended to infinity, a sharp boundary is obtained for the domain of existence of classical reality. The last is treated as separable empirical reality following d'Espagnat, described by a mathematical superstructure over quantum dynamics for the universal wave function. Being empirical, this reality is constructed in terms of both fundamental notions and characteristics of observers. It is presupposed that considered observers perceive the world as a system of collective degrees of freedom that are inherently dissipative because of interaction with thermal degrees of freedom. Relevant problems of foundation of statistical physics are considered. A feasible example is given of a macroscopic system not admitting such classical reality. The article contains a concise survey of some relevant domains: quantum and classical Bell-type inequalities; universal wave function; approaches to quantum description of macroscopic world, with emphasis on dissipation; spontaneous reduction models; experimental tests of the universal validity of the quantum theory.
TL;DR: The Casimir force between two dielectric slabs of finite thickness is calculated for the case of dissipative media as a continuous field of quantum harmonic oscillators interacting with the heat bath.
Abstract: The Casimir force between two dielectric slabs of finite thickness is calculated for the case of dissipative media. The medium is modeled as a continuous field of quantum harmonic oscillators interacting with the heat bath. The electromagnetic field inside and outside the cavity formed by the plates is found for the ground state of the coupled system, and its pressure is calculated. Two terms in the expression for the Casimir force are distinguished. One is the electromagnetic vacuum pressure, which is the only contribution in the case of lossless media. The other arises from the Langevin forces that appear together with the damping as the result of the interaction of atoms with the heat bath. It is shown that both contributions are necessary in order to arrive at a finite result.
TL;DR: In this paper, a theoretical study of dissipative scattering in mesoscopic systems is presented, where exact expressions for the transmission and reflection probabilities between the various leads and channels are derived in terms of dressed two-particle Green's functions.
TL;DR: It is shown that the geometrical (Berry) phases discovered in Hamiltonian systems can also be defined as resulting from parallel transportation of vectors for nonlinear dissipative systems with cyclic attractors.
Abstract: We show that the geometrical (Berry) phases discovered in Hamiltonian systems can also be defined as resulting from parallel transportation of vectors for nonlinear dissipative systems with cyclic attractors. If the nonlinear dissipative systems possess a certain kind of asymptotic solution defined in this Letter, the phase and amplitude accumulation of a geometrical type can be defined. Detuned one- and two-photon lasers showing periodic intensity pulsations are taken as examples of such systems.