Conserved densities for linear evolution systems

A general discussion of the conservation laws for simple linear evolution systems is presented. The analysis is based upon an extension of the Gel'fand-Dikii symbolic algorithm to cover pseudo-differential operators. These techniques are applied to obtain all the conserved densities [u] for the free Klein-Gordon and Dirac equations with nonzero mass.     

Constants of motion in NMR spectroscopy

We present a general method for constructing a subset of the constants of motion in terms of products of spin operators. These operators are then used to give insight into the multi-spin orders comprising the quasi-equilibrium state formed under a Jeener-Broekaert sequence in small, dipolar-coupled, spin systems. We further show that constants of motion that represent single-quantum coherences are present due to the symmetry of the dipolar Hamiltonian under 180 degrees spin rotations, and that such coherences contribute a DC component to the FID which vanishes in the absence of the flip-flop terms and is only present for spin clusters with an odd number of spins.     

Constants of the motion in lagrangian mechanics

Two points of view of the relationship between symmetries of a dynamical system and constants of the motion, in the Lagrangian framework, are compared. The first point of view is that associated with Noether's theorem, the second, with the Cartan form approach to Lagrangian mechanics. It is argued that the second is more satisfactory.     

The decoupling of defective linear dynamical systems in free motion

It was demonstrated in two earlier papers that there exists a real, linear, time-varying transformation that decouples any non-defective linear dynamical system in free vibration in the configuration space. As an extension of this work, the present paper represents the first systematic effort to decouple defective systems. It is shown that the decoupling of defective systems is a rather delicate procedure that depends on the multiplicities of the system eigenvalues. While any defective system can be decoupled with the eigenvalues kept invariant, the geometric multiplicities of these eigenvalues may not be preserved. Several numerical examples are provided to illustrate the theoretical developments.     

Constants of the motion for the Benjamin-Ono and related equations

It is shown that the Benjamin-Ono equation and higher order equations of the same kind have an infinite series of infinite sets of constants of the motion. Apart from the, already known, first set these constants depend explicitly on time.     

Constants of motion of the four-particle Calogero model

We present the explicit expressions of the complete set of constants of motion of four-particle Calogero model with excluded center of mass, i.e. of the A ₃ rational Calogero model. Then we find the constants of motion of its spherical part, defining two-dimensional 12-center spherical oscillator, with the force centers located at the vertexes of cuboctahedron.     

On the transition to aperiodic motion in linear systems with strong relaxation

The Bloch equations are shown to possess purely aperiodic solutions at intermediate values of the transverse relaxation coefficient only. We present also a simple example of a mechanical system where the regions of aperiodic motion are separated by the region of damped oscillations.     

Equations of motion for continuum systems

We construct equations of motion for anN-component continuum. The basic assumption is that the dynamical vector field is the sum of two terms: a conservative term, being a Hamiltonian vector field associated with the energy function of the system; and a dissipative term, being a gradient vector field associated with a family of functions. The resulting equations satisfy the usual conservation laws for continuum systems, and, moreover, reduce to the standard fluid equations when the continuum is a fluid.     

Output regulation for linear multi-agent systems with unmeasurable nodesOutput regulation for linear multi-agent systems with unmeasurable nodesOutput regulation for linear multi-agent systems with unmeasurable nodes

The output regulation of linear multi-agent systems with partial unmeasurable agents is investigated in this paper. All the agents except the exosystem can be classified into two groups. Agents in the first group can be measured by themselves and their neighbors. State variables are not fully accessible for direct communication and full order Luenberger observers are constructed for the unmeasurable agents. We give a state feedback control law to solve the output regulation problem under the communication topologies based on both measurable and unmeasurable agents. The heterogeneous agents＇ synchronization problem is a general case of our results. Finally, examples are utilized to show the effectiveness of the obtained results.     

Quasi-canonicalization for linear homogeneous nonholonomic systems

For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ∧ dξμ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates πμand quasi-momenta ξμ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates πμby a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton–Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton–Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton–Jacobi method.     

SLIM-a formalism for linear coupled systems

A SLIM formalism to deal with a general, linearly coupled accelerator lattice is summarized. Its application to a wide range of accelerator calculations is emphasized.     

Constants of motion in local field theory (Coleman's theorem revisited)

We analyze the space integralsQ=d ³ x(x) of finitely localized densities . It turns out that the time translated operatorsQ(t) are polynomials int ifQ annihilates the vacuum. In particular,Q(t) =Q in models with short-range forces and complete particle interpretation. These results are valid in the Haag-Araki framework of field theory as well as in the Wightman formalism. Lorentz covariance is not needed in the proofs.     

Model for Brownian motion in soft-jammed systems

Brownian motion in soft-jammed systems (pastes) is directly described by taking into account the specific mechanical characteristics of the material surrounding the moving object. In particular we obtain explicit forms for the fluctuation-dissipation equation and the specific characteristics of diffusion through a soft-jammed system.     

Equivalent linear models for non-linear non-autonomous systems

Equivalence between a class of non-linear non-autonomous systems of second order and a linear model of lower order is established through a differential transformation relation. It is shown that this equivalence can be established only under a certain constraint on the non-linear functional parameters of the given system. The equivalence automatically leads to the first integral which then can be analyzed further to obtain the response of the system. The feasibility of obtaining closed form solutions through such analysis is illustrated by considering certain sub-classes of systems. Further, the practical value of the technique is demonstrated through an example.     

A parabolic linear evolution equation for cellular detonation instability

Using the combined limits of a large activation energy and a ratio of specific heats close to unity, a dispersion relation has recently been derived which governs the stability of a steady Chapman - Jouguet detonation wave to two-dimensional linear disturbances. The analysis considers instability evolution time scales that are long on the time scale of fluid particle passage through the main reaction layer. In the following, a simplified polynomial form of the dispersion relation is derived under an appropriate choice of a distinguished limit between an instability evolution time scale that is long on the time scale of particle passage through the induction zone and a transverse disturbance wavelength that is long compared to the hydrodynamic thickness of the induction zone. A third order in time, sixth order in space, parabolic linear evolution equation is derived which governs the initial dynamics of cellular detonation formation. The linear dispersion relation is shown to have the properties of a most unstable wavenumber, leading to a theoretical prediction of the initial detonation cell spacing and a wavenumber above which all disturbances decay, eliminating the growth of small-wavelength perturbations. The role played by the curvature of the detonation front in the dynamics of the cellular instability is also highlighted.     

Chaotic particle motion under linear surface waves

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos. (c) 1996 American Institute of Physics.