Comparing ordered-entry queues with heterogeneous servers

We study a queueing system withm exponential servers with distinct service rates. Jobs arrive at the system following an arbitrary point process. Arrived jobs receive service at the first unoccupied server (if any) according to an entry order , which is a permutation of the integers 1, 2,...,m. The system has a finite buffer capacity. When the buffer limit is reached, arrivals will be blocked. Blocked jobs will either be lost or come back as New arrivals after a random travel time. We are concerned with the dynamic stochastic behavior of the system under different entry orders. A partial ordering is established among entry orders, and is shown to result in some quite strong orderings among the associated stochastic processes that reflect the congestion and the service characteristics of the system. The results developed here complement existing comparison results for queues with homogeneous servers, and can be applied to aid the design of conveyor and communication systems.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

On the invariant measures for the two-dimensional euler flow

It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

Statistical replacement for systems with delta-correlated fluctuations

Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable.     

Green Chemistry and Modern Technology

The basic principles, approaches, and early achievements of green chemistry are considered. The definition of green chemistry as a branch of chemistry that studies the laws of passing of chemical reactions and the properties of substances participating in such reactions, with the aim of acquiring basic knowledge that provides a basis for designing chemical technologies that eliminate (sharply curtail) the use and production of materials that pose a risk to the environment.     

Accurate Gaussian basis sets for the H2O molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H₂O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H₂O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.     

Organic templates for the generation of inorganic materials

Mankind's fascination with shapes and patterns, many examples of which come from nature, has greatly influenced areas such as art and architecture. Science too has long since been interested in the origin of shapes and structures found in nature. Whereas organic chemistry in general, and supramolecular chemistry especially, has been very successful in creating large superstructures of often stunning morphology, inorganic chemistry has lagged behind. Over the last decade, however, researchers in various fields of chemistry have been studying novel methods through which the shape of inorganic materials can be controlled at the micro- or even nanoscopic level. A method that has proven very successful is the formation of inorganic structures under the influence of (bio)organic templates, which has resulted in the generation of a large variety of structured inorganic structures that are currently unattainable through any other method.