Chip-Firing Games on Directed Graphs

We consider the following (solitary) game: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. We extend to directed graphs several results on the undirected version obtained earlier by the authors, P. Shor, and G. Tardos, and we discuss some new topics such as periodicity, reachability, and probabilistic aspects.Among the new results specifically concerning digraphs, we relate the length of the shortest period of an infinite game to the length of the longest terminating game, and also to the access time of random walks on the same graph. These questions involve a study of the Laplace operator for directed graphs. We show that for many graphs, in particular for undirected graphs, the problem whether a given position of the chips can be reached from the initial position is polynomial time solvable.Finally, we show how the basic properties of the probabilistic abacus can be derived from our results.     

On the treatment of the pairing interaction in the particle-rotor model

Different ways of treating the pairing interaction in the particle-rotor model are discussed and compared in a model which can be solved exactly. Special attention is paid to the interaction between the yrast and yrare bands as function of the shell filling.     

Vanishing of local homology

 We study the vanishing properties of local homology of complexes of modules without assuming that its homology is artinian. Using vanishing results for local homology and cohomology we prove new vanishing results for Ext- and Tor-modules. Received: 1 August 2002; in final form: 23 September 2002 / Published online: 16 May 2003 Mathematics Subject Classification (1991): 13C12, 13D07, 13D45.     

Fast ortho-para conversion of H2 adsorbed at copper surface step atoms

Ortho-para conversion of H2 adsorbed at the step atoms of a Cu(510) surface proceeds with a short conversion time constant around 1 s as observed in electron-energy-loss measurements of rotational populations. We suggest that this rapid conversion is related to the special character of the adsorption state, which involves a short H2-Cu bond length of 1.8 A. On the flat Cu(100) surface, conversion is found to occur at active sites, most likely step atoms.     

Acoustic characteristics of a heavy duty vehicle cooling module

Studies dedicated to the determination of acoustic characteristics of an automotive cooling package are presented. A shrouded subsonic axial fan is mounted in a wall separating an anechoic- and a reverberation room. This enables a unique separation of the up- and downstream sound fields. Microphone measurements were acquired of the radiated sound as a function of rotational speed, fan type and components included in the cooling module. The aim of the present work is to investigate the effect of a closely mounted radiator upstream of the impeller on the SPL spectral distribution. Upon examination of the SPL spectral shape, features linked specifically to the source and system are revealed. The properties of a reverberant sound field combined with the method of spectral decomposition permit an estimation of the source spectral distribution and the acoustic transfer response, respectively. Additionally, purely intrinsic acoustic properties of the radiator are scrutinized by standardized ISO methods. A new methodology comprising a dipole sound source is adopted to circumvent limitation of transmission loss measurement in the low frequency range. The sound attenuation caused by the radiator alone was found to be negligible.     

Time-reversible Born-Oppenheimer molecular dynamics

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the nonlinearity and incompleteness of the self-consistent field procedure. With a time-reversible lossless propagation the simulated dynamics is stabilized with respect to a systematic long-term energy drift and the number of self-consistency cycles can be kept low thanks to a good initial guess given from the electronic propagation. The proposed molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation, which preserves a detailed balance between propagation forwards and backwards in time.     

Molecular adsorption and growth of n-butane adlayers on Pt(1 1 1)

The molecular adsorption of n-butane and the growth of n-butane adlayers on Pt(1 1 1) was investigated using molecular beam techniques, temperature-programmed desorption (TPD) and low-energy electron diffraction (LEED). It is found that as the surface coverage of n-butane increases, structural changes occur in the adlayer at surface temperatures near 98 K that are accompanied by changes in the binding energy and mobility of the adsorbed species. The film growth process can be divided into four distinct coverage regimes. At low coverages (θ<0.14 ML, where 1 ML is defined as one butane molecule per Pt atom) a disordered monolayer forms in which the butane molecules prefer to lie parallel to the surface in order to minimize their binding energy. At coverages from 0.14 to 0.20 ML, ordered regions develop within the monolayer in which the butane molecules also lie parallel to the surface. The binding energy in the ordered phase is lower than that in the disordered phase due to repulsive intermolecular interactions. A more densely-packed ordered phase begins to form at 98 K after the low-coverage ordered phase saturates at 0.20 ML. The experimental results suggest that the n-butane molecules tilt away from the surface in the high-coverage ordered phase. Finally, a disordered second layer phase forms after the high coverage ordered phase saturates at 0.35 ML. The molecules in the second layer are very mobile at 98 K and rapidly diffuse to the edges of the beam spot. Interchange of molecules between the second layer and ordered monolayer is found to govern the net rate of second layer diffusion at surface temperatures less than 133 K. The adsorption probability of n-butane on Pt(1 1 1) continuously increases with increasing coverage, with no significant dependencies on the structure of the n-butane adlayer. This finding indicates that the long-range arrangements and molecular orientations of a mobile alkane adlayer have a negligible influence on the intrinsic adsorption dynamics, suggesting that the energy transfer processes that facilitate adsorption are highly localized.     

On the optimum set of polarization measurements for the scattering of two indentical fermions to determine the helicity amplitudes

The polarization asymmetries related to usual polarizations combine at least 4 different helicity amplitudes. The introduction of ±45° inclined transverse polarizations allows us to obtain the complete set of new polarization asymmetries combining only up to 3 helicity amplitudes. There are no further polarization asymmetries depending on a smaller number of helicity amplitudes. These expressions are most economical to determine the helicity amplitudes from observed data. Some of them are suitable to study especially the spin-flip effects. We give a complete Table of all such polarization asymmetries.     

QED polarization asymmetries fore + e − scattering due to helicity flips

The polarization asymmetries for thee ⁺ e ^? scattering with polarized incoming and outgoing beams, which are proportional to the amplitudes? ₅ describing one helicity flip and? ₅ describing two helicity flips, have been calculated including their pure QED radiative corrections. These asymmetries are partly large and can be observed well at low energies.