Metallic clusters in the AlN ceramic

Characterization of the local environment of metallic ions (Cu, Fe, Ti, Ni and Er) implanted in the ceramic matrix AlN have led us to conclude that the heat of formation (\Delta H) of the implanted ion nitride (I-N) is the parameter which has to be considered in order to predict the final system. When ΔH_I-N is negative, bonds between the implanted ion and nitrogen atoms are formed, when ΔH_I-N is positive, clusters of the implanted ion are formed. Moreover, we give some physical characteristics of the Cu and Ni clusters in the AlN matrix and show the differences between imbedded and deposited clusters of the same size. This revised version was published online in August 2006 with corrections to the Cover Date.     

A method of autonomous orbit determination for satellite using star sensor

1 Introduction Autonomous orbit determination of satellite means that orbit determination is solely finished on board, independent of the observation of ground system. Study on autono-mous orbit determination of satellite has been very hot in the field of orbit determination currently internationally due to its significance in application. There are two common ways of autonomous orbit determination internationally. One is autonomous orbit deter-mination based on navigation system, such as on-b…     

Relativistic star clusters with high central redshift

Collisionless star clusters in dynamical equilibrium are of current interest in general relativity and astrophysics. A step-function distribution is chosen for star clusters. The corresponding equation of state is analogous to a Fermi-gas equation. These clusters are found to be pulsationally unstable for a central redshift ofZ _c ⩾ 0·54. Further, a model of clusters is developed in which the core has an extremely relativistic equation of state. These structures are unstable forZ _c ⩾ 2·55 when we use Chandrasekhar’s technique to study their pulsational stability.     

Integrable and nonintegrable classical spin clusters

This study investigates the nonlinear dynamics of a pair of exchange-coupled spins with biaxial exchange and single-site anisotropy. It represents a Hamiltonian system with 2 degrees of freedom for which we have already established the (nontrivial) integrability criteria and constructed the integrals of the motion provided they exist. Here we present a comparative study of the phase-space trajectories for two specific models with the same symmetry properties, one of which (the XY model with exchange anisotropy) is integrable, and the other (the XY model with single-site anisotropy) nonintegrable. In the integrable model, the integrals of the motion (analytic invariants) can be reconstructed numerically by means of time averages of dynamical variables over all trajectories. In the nonintegrable model, such time averages over trajectories define nonanalytic invariants, where the nonanalyticities are associated with the presence of chaotic trajectories. A prominent feature in the nonintegrable model is the occurrence of very long time scales caused by the presence of low-flux cantori, which form sticky coats on the boundary between chaotic regions and regular islands or leaky walls between different chaotic regions. These cantori dominate the convergence properties of time averages and presumably determine the long-time asymptotic properties of dynamic correlation functions. Finally, we present a special class of integrable systems containing arbitrarily many spins coupled by general biaxial exchange anisotropy.     

Integrable and nonintegrable classical spin clusters

The nonlinear dynamics is investigated for a system ofN classical spins. This represents a Hamiltonian system withN degrees of freedom. According to the Liouville theorem, the complete integrability of such a system requires the existence ofN independent integrals of the motion which are mutually in involution. As a basis for the investigation of regular and chaotic spin motions, we have examined in detail the problem of integrability of a two-spin system. It represents the simplest autonomous spin system for which the integrability problem is nontrivial. We have shown that a pair of spins coupled by an anisotropic exchange interaction represents a completely integrable system for any values of the coupling constants. The second integral of the motion (in addition to the Hamiltonian), which ensures the complete integrability, turns out to be quadratic in the spin variables. If, in addition to the exchange anisotropy also singlesite anisotropy terms are included in the two-spin Hamiltonian, a second integral of the motion quadratic in the spin variables exists and thus guarantees integrability, only if the model constants satisfy a certain condition. Our numerical calculations strongly suggest that the violation of this condition implies not only the nonexistence of a quadratic integral, but the nonexistence of a second independent integral of motion in general. Finally, as an example of a completely integrableN-spin system we present the Kittel-Shore model of uniformly interacting spins, for which we have constructed theN independent integrals in involution as well as the action-angle variables explicitly.     

Quantum spectra and classical periodic orbit in the cubic billiard

Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.     

Percolation for low energy clusters and discrete symmetry breaking in classical spin systems

We consider classical lattice systems in two or more dimensions with general state space and with short-range interactions. It is shown that percolation is a general feature of these systems: If the temperature is sufficiently low, then almost surely with respect to some equilibrium state there is an infinite cluster of spins trying to form a ground state. For systems having several stable sets of symmetry-related ground states we show that at low temperatures spontaneous symmetry breaking occurs because in a two-dimensional subsystem there is a unique infinite cluster of this type.     

An effective potential for classical Yang-Mills fields as outline for bifurcation on gauge orbit space

Classical Yang-Mills (Y.M.) equations with static external sources are formulated as a Hamiltonian system with gauge symmetry in A₀ = 0 gauge. Using the concept of a “momentum mapping” (J. Marsden and A. Weinstein, Rep. Math. Phys.5 (1974), 121) on symplectic manifolds with symmetry, an analogue of centrifugal potential of a mass point in a spherically symmetric potential is derived. This gives rise to an effective potentialV_eff, whose critical points are rigorously proved to be in one-to-one correspondence with static Y.M. solutions. V_eff additionally depends on the prescribed external source ?, which is as a constant of motion analogous to angular moment of the mass point. Thus bifurcation of static solutions is caused by bifurcation of critical points of V_eff under variation of the external parameter ?. Some closing remarks on dynamics and stability on gauge orbit space are added.     

Radial-fluctuation-induced stabilization of the ordered state in two-dimensional classical clusters

Melting of two-dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined either by a circular hard wall or by a parabolic external potential and interact through a dipole or a screened Coulomb potential. We found that, with decreasing strength of the interparticle interaction, clusters with a short-range interparticle interaction and confined by a hard wall exhibit a reentrant behavior in its orientational order.     

A classical reactive potential for molecular clusters of sulphuric acid and water

We present a two-state empirical valence bond (EVB) potential describing interactions between sulphuric acid and water molecules and designed to model proton transfer between them within a classical dynamical framework. The potential has been developed in order to study the properties of molecular clusters of these species, which are thought to be relevant to atmospheric aerosol nucleation. The particle swarm optimisation method has been used to fit the parameters of the EVB model to density functional theory (DFT) calculations. Features of the parametrised model and DFT data are compared and found to be in satisfactory agreement. In particular, it is found that a single sulphuric acid molecule will donate a proton when clustered with four water molecules at 300 K and that this threshold is temperature dependent.     

Evolution of star clusters with a mass distribution of binaries

Summary The dynamical evolution of star clusters with a initial population of binaries strongly depends on the parameters of the bounded pairs. We performed computational simulation with directN-body codes, on models withN=300 objects, with initial fraction of 20% of binaries with the same orbital semi-axis and with a Salpeter mass spectrum. The results are compared with previous analysis on similar equal-mass star models. The calculation points out that binaries with different mass companions determine an enhanced and sudden expansion of the system with neither core collapse nor central mass segregation. Paper presented at the 2° Convegno Nazionale di Fisica Cosmica, held at L'Aquila, 29 May – 2 June 1984.     

Evidence for a compressed fluid phase of Xe clusters

We report on the formation and detection of a compressed fluid phase of Xe clusters in as- implanted Si, at room temperature. The simultaneous structural characterization of the Xe clusters and of the Si matrix was performed by X-ray diffraction at grazing incidence coupled with two-dimensional detection; in both cases, the nearest-neighbor distance and the coordination were obtained. In order to investigate the early stage of the atomic inclusion and the cluster segregation, the average compression and size of Xe fluid clusters within the amorphous Si matrix were explained within the simple Hard Sphere model. Received 4 September 2000 and Received in final form 13 December 2000