A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

Interpretation of Nuclear Quadrupole Resonance Spectra in Doped La2_2CuO4_4

The nuclear quadrupole resonance (NQR) spectrum of strontium doped La$_2$CuO$_4$ surprisingly resembles the NQR spectrum of La$_2$CuO$_4$ doped with excess oxygen, both spectra being dominated by a main peak and one principal satellite peak at similar frequencies. Using first-principles cluster calculations this is investigated here by calculating the electric field gradient (EFG) at the central copper site of the cluster after replacing a lanthanum atom in the cluster with a strontium atom or adding an interstitial oxygen to the cluster. In each case the EFG was increased by approximately 10 % leading unexpectedly to the explanation that the NQR spectra are only accidentally similar and the origins are quite different. Additionally the widths of the peaks in the NQR spectra are explained by the different EFG of copper centres remote from the impurity. A model, based on holes moving rapidly across the planar oxygen atoms, is proposed to explain the observed increase in frequency of both the main and satellite peaks in the NQR spectrum as the doping concentration is increased

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.Comment: 4 pages, 4 figure

Velocity Correlations, Diffusion and Stochasticity in a One-Dimensional System

We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a non-vanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a $t^{-3}$ tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.Comment: 22 files, 2 eps figures. Submitted to PR

How to quantify deterministic and random influences on the statistics of the foreign exchange market

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can be estimated. Finally, we present an explicite Fokker-Planck equation which models very precisely the empirical probabilitiy distributions.Comment: 3 figure

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199

Are galactic disks dynamically influenced by dust?

Dynamically cold components are well known to destabilize hotter, even much more massive components. In this paper we studied the dynamical influence of a cold dust component on the gaseous phase in the central regions of galactic disks. We performed two-dimensional hydrodynamical simulations for flat multi-component disks embedded in a combined static stellar and dark matter potential. The pressure-free dust component is coupled to the gas by a drag force depending on their velocity difference. It turned out that the most unstable regions are those with either a low or near to minimum Toomre parameter or with rigid rotation, i.e. the central area. In that regions the dust-free disks become most unstable for high azimuthal modes (m~8), whereas in dusty disks all modes have a similar amplitude resulting in a patchy appearance. The structures in the dust have a larger contrast between arm and inter-arm regions than those of the gas. The dust peaks are frequently correlated with peaks of the gas distribution, but they do not necessarily coincide with them. Therefore, a large scatter in the dust-to-gas ratios is expected. The appearance of the dust is more cellular (i.e. sometimes connecting different spiral features), whereas the gas is organized in a multi-armed spiral structure. An admixture of 2% dust destabilizes gaseous disks substantially, whereas dust-to-gas ratios below 1% have no influence on the evolution of the gaseous disk. For a high dust-to-gas ratio of 10% the instabilities reach a saturation level already after 30 Myr.Comment: 21 pages including 24 figures (some figures degraded in quality), in press in Astronomy & Astrophysics 418, 959(2004), A&A version available at http://www.edpsciences.org/articles/aa/full/2004/18/aa0047/aa0047.htm

Angle-resolved photoemission in doped charge-transfer Mott insulators

A theory of angle-resolved photoemission (ARPES) in doped cuprates and other charge-transfer Mott insulators is developed taking into account the realistic (LDA+U) band structure, (bi)polaron formation due to the strong electron-phonon interaction, and a random field potential. In most of these materials the first band to be doped is the oxygen band inside the Mott-Hubbard gap. We derive the coherent part of the ARPES spectra with the oxygen hole spectral function calculated in the non-crossing (ladder) approximation and with the exact spectral function of a one-dimensional hole in a random potential. Some unusual features of ARPES including the polarisation dependence and spectral shape in YBa2Cu3O7 and YBa2Cu4O8 are described without any Fermi-surface, large or small. The theory is compatible with the doping dependence of kinetic and thermodynamic properties of cuprates as well as with the d-wave symmetry of the superconducting order parameter.Comment: 8 pages (RevTeX), 10 figures, submitted to Phys. Rev.

Flux-Induced Vortex in Mesoscopic Superconducting Loops

We predict the existence of a quantum vortex for an unusual situation. We study the order parameter in doubly connected superconducting samples embedded in a uniform magnetic field. For samples with perfect cylindrical symmetry, the order parameter has been known for long and no vortices are present in the linear regime. However, if the sample is not symmetric, there exist ranges of the field for which the order parameter vanishes along a line, parallel to the field. In many respects, the behavior of this line is qualitatively different from that of the vortices encountered in type II superconductivity. For samples with mirror symmetry, this flux-induced vortex appears at the thin side for small fluxes and at the opposite side for large fluxes. We propose direct and indirect experimental methods which could test our predictions.Comment: 6 pages, Latex, 4 figs., uses RevTex, extended to situations far from cylindrical symmetr

Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.