Finite Lifetime Eigenfunctions of Coupled Systems of Harmonic Oscillators

We consider a vector-valued Hermite-type basis for which the eigenvalue problem associated to the operator H _A,B :=B(; _x ² )+Ax ² acting on becomes a three-terms recurrence. Here A and B are 2 × 2 constant positive definite matrices. Our main result provides an explicit characterization of the eigenvectors of H _A,B that lie in the span of the first four elements of this basis when AB BA.This revised version was published online in March 2005 with corrections to the cover date.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

Monitoring nanoparticle formation during laser ablation of graphite in an atmospheric-pressure ambient

Excimer laser ablation of highly oriented pyrolytic graphite (HOPG) was performed at atmospheric pressure in an N₂ and in an air ambient. During the ablation, nanoparticles condensed from the material ejecta, and their size distribution was monitored in the gas phase by a Differential Mobility Analyzer (DMA) in combination with a Condensation Particle Counter (CPC). Size distributions obtained at different laser repetition rates revealed that the interaction between subsequent laser pulses and formed particles became significant above 15 Hz. This interaction resulted in laser heating, leading to considerable evaporation and a decrease in the size of the particles. X-ray photoelectron spectroscopy revealed that approximately 8% nitrogen was incorporated into the CN_x particles generated in the N₂ ambient, and that the nitrogen was mostly bonded to sp³-hybridized carbon. Monodisperse particles were also deposited and were analyzed by means of Raman spectroscopy to monitor size-induced effects. PACS 81.07.-b; 61.46.+w; 79.70.+q     

Experimental investigation of Risken–Nummedal–Graham–Haken laser instability in fiber ring lasers

It has been suggested (by Pessina et al. in 1997) that the observed spontaneous mode beating of erbium-doped-fiber ring lasers can be explained as the multimode instability described in 1968 by Risken and Nummedal and by Graham and Haken (the RNGH instability), which is based on Rabi-splitting-induced gain. If true, this would constitute the first ever example of this instability in an actual experiment. We test the hypothesis through a quantitative experimental investigation. We demonstrate that there is indeed a clear, marked onset of the instability, a fact that went unnoticed in all previous experiments because it is very close to the lasing threshold. We intentionally raise cavity loss to better separate onset of lasing and of instability. We obtain quantitative information on the instability onset. An interpretation as the predicted second threshold is reasonable provided inhomogeneous gain line broadening is taken into account. We also observe that instability above its onset exists only intermittently; this may hint at a subcritical bifurcation and noise-driven transitions. In any event, the RNGH mechanism is present, if not in a pure form. PACS 42.65.Sf; 42.60.Mi; 42.55.Wd     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Geometry of an Accelerated Rotating Disk

We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the theory of Special Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in a Fermi reference. A numerical integration of these equations for a generic initial value problem is made up and the results are compared with those obtained in other works.     

Ab initio study of 40Ca with an importance-truncated no-core shell model

We propose an importance truncation scheme for no-core shell model or configuration interaction approaches, which enables converged calculations for nuclei well beyond the p shell. It is based on an a priori measure for the importance of individual basis states constructed by means of many-body perturbation theory. Only the physically relevant states of the no-core model space are considered, which leads to a dramatic reduction of the basis dimension. We analyze the validity and efficiency of this truncation scheme using different realistic nucleon-nucleon interactions and compare to conventional no-core shell model calculations for 4He and 16O. Then, we present first converged calculations for the ground state of 40Ca within no-core model spaces including up to 16 PlanckOmega excitations using realistic low-momentum interactions. The scheme is universal and can be easily applied to other quantum many-body problems.     

Longitudinal-transverse separations of deep-inelastic structure functions at low Q2 for hydrogen and deuterium

We report on a study of the longitudinal to transverse cross section ratio, R=sigmaL/sigmaT, at low values of x and Q2, as determined from inclusive inelastic electron-hydrogen and electron-deuterium scattering data from Jefferson Laboratory Hall C spanning the four-momentum transfer range 0.06相似文献   

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Small-angle X-ray scattering on spinodal,nucleotic or coarsening processes in two-phase systems containing spherical,fibrillar or lamellar inhomogeneities

We study the effects of some of the most important and typical structural changes in two-phase systems on selected structural parameters obtained from small-angle x-ray scattering (SAXS) measurements. To limit the present study, it was assumed that the Phase, 1, embedded in the matrix

1. is monodispersed and homogeneous,
2. possesses one of the three most extreme shapes (spherical, fibrillar or lamellar) and
3. changes its behaviour

1. through type change (spinodal or nucleotic or coarsening), without changing the shape,
2. through a change of the shape only, or
3. through a) (type change) and b) (shape change) simultaneously.

To find the type of change for three basically different shapes of Phase 1 and to calculate its intensity (amount of the change) the following three SAXS parameters must be compared before and after the treatment of the system:

1. chord lengthl ₁ (and/or radius of gyrationR),
2. volume partw ₁ of the Phase 1, and
3. relative inner surfaceS _v of the system.

It is shown by this comparison that by the pure type change in the case of

1. spinodal change, all three SAXRS parameters are increasing or decreasing simultaneously and proportional to a power of the intensity of the change,
2. nucleotic change,l ₁ (and/orR) is unchanged, the other two (w ₁ andS _v ) are increasing or decreasing simultaneously and directly proportional to the intensity,
3. coarsening change,w ₁ is unchanged and anincreasing ofl ₁ is always accompanied by adecreasing ofS _v and vice versa.

In addition to this type change, the cases of mere changes of the shape (“shape change”) and finally of simultaneous type and/or shape change are studied. For the case of pure shape change the alteration of the dimensions (chord lengthl ₁ and/or radius of gyrationR) must be followed. The limitations of the analyses of the simultaneous type and/or shape change are discussed in detail.