Structural characterization of decomposition in rate-insensitive stochastic Petri nets

This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as $S\Pi^2$ nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of $T$-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its $T$-invariants

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method

Contributions of Repulsive and Attractive Interactions to Nematic Order

Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not unprecedented; what is perhaps new is the focus on the understanding of nematics in the high density limit. There, the orientational probability distribution is shown to exhibit a unique feature: it has compact support on configuration space. As attractive interactions are turned on, the behavior changes, and at a critical attractive interaction strength, thermotropic behavior of the Maier-Saupe type is attained.Comment: 14 pages, 4 figure

All-electron molecular Dirac-Hartree-Fock calculations: The group 4 tetrahydrides CH4, SiH4, GeH4, SnH4 and PbH4

A basis-set-expansion Dirac-Hartree-Fock program for molecules is described. Bond lengths and harmonic frequencies are presented for the ground states of the group 4 tetrahydrides, CH4, SiH4, GeH4, SnH4, and PbH4. The results are compared with relativistic effective core potential (RECP) calculations, first-order perturbation theory (PT) calculations and with experimental data. The bond lengths are well predicted by first-order perturbation theory for all molecules, but non of the RECP's considered provides a consistent prediction. Perturbation theory overestimates the relativistic correction to the harmonic frequencies; the RECP calculations underestimate the correction

Minimising Numbers of Losses and Abandonments in Small Call Centres Under a Transient Regime

In this paper, we show how to calculate transient performance measures in models for small call centres that employ skills-based routing. In particular, we calculate the expected number of customer losses and call abandonments in a fixed time. We use the results to compare how call allocation policies can minimise the expected numbers of losses and abandonments, and make recommendations about which policies should be employed

Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network, and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution

A simple interpretation of the Fe2(-) photoelectron spectrum

The photoelectron spectrum of Fe2(-) can be simply interpreted in terms of electron detachment from the mildly bonding 4s sigma sup * sub u orbital of a (4s sigma sub s)(sup 2) (4s sigma sup * sub u)(sup 2) (3d)(sup 13) anion. This interpretation implies a (4s sigma sub g)(sup 2) (4s sigma sup * sub u)(sup1) (3d)(sup13) configuration for the ground state of Fe2, correlating with one ground state (4s2 3d6) and one excited state (4s1 3d7) Fe atom. A comparison of the bond length and vibrational frequency of Fe2 to values for transition metal dimers containing single 4s-4s bonds is suggestive of 3d-3d bonding in this molecule. The results of preliminary full-valence configuration interaction calculations provide stron support for the proposed Fe2 and Fe2(-) configurations

Experimental measurement of focused wave group and solitary wave overtopping

Prediction of individual wave overtopping events is important in assessing danger to life and property, but data are sparse and hydrodynamic understanding is lacking. Laboratory-scale waves of three distinct types were generated at the Coastal Research Facility to model extreme waves overtopping a trapezoidal embankment. These comprised wave groups of compact form, wave groups embedded in a background wave field, and a solitary wave. The inshore wave propagation was measured and the time variation of overtopping rate estimated. The total volume overtopped was measured directly. The experiments provide well-defined data without uncertainty due to the effect of reflection on the incident wave train. The dependence of overtopping on a range of wave shapes is thus determined and the influence of wave-wave interactions on overtopping assessed. It was found that extreme overtopping may arise from focused waves with deep troughs rather than large crests. Furthermore, overtopping waves can be generated from small wave packets without affecting the applicability of results to cases in which there are surrounding waves. Finally, overtopping from a solitary wave is comparable with overtopping from focused wave groups of the same amplitude. © 2011 Copyright International Association for Hydro-Environment Engineering and Research

Density functional theory for dense nematics with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it fails to provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature: it vanishes on a nonzero measure set in orientational space