Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.     

Nearly zero ultraflattened dispersion in photonic crystal fibers

We present a procedure for achieving photonic crystal fibers with nearly zero ultraflattened group-velocity dispersion. Systematic knowledge of the special guiding properties of these fibers permits the achievement of qualitatively novel dispersion curves. Unlike the behavior of conventional fibers, this new type of dispersion behavior permits remarkably improved suppression of third-order dispersion, particularly in the low-dispersion domain.     

MULTIQ: A Queueing Model for FMSs with Several Pallet Types

Analytical modelling of the work flow through flexible manufacturing systems (FMSs), based on closed queueing network models, has been successfully applied to the early stages of design and analysis of FMSs. This paper describes the advantages of using multiple job-class closed queueing networks for modelling realistic situations occurring in FMSs. The general modelling of FMSs by closed queueing networks is first reviewed. The way Solberg's CAN-Q—a single job-class queueing-based package—deals with several part types is clarified. A new model called MULTIQ, allowing multiple pallet types, each of which is used by several part types, is proposed. Results are derived using the data from an existing FMS. The use of the MULTIQ model for optimization purposes is suggested by some examples.     

Effect of defect scattering on anisotropic phonon density in metal films

The effect of defect phonon scattering on the spatial dependence of the distribution of phonons generated by Joule heating in metal films is studied. This interaction process is shown to significantly modify the dependence on the direction of propagation of the phonon energy density spectrum.     

Contributions to the theory of stochastic programming

Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.This work was supported in part by the Institute of Economic Planning, Budapest.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands, under the title Programming under probabilistic constraints and programming under constraints involving conditional expectations.     

On a dual submanifold homomorphism

In this paper we develop a technique to study the homomorphisma: MU _* (B U₁)→M U_*?2 (B U₁) defined by assigning to the class off: M→B U ₁ the class off _oi: N→B U₁, wherei: N→M is the submanifold dual tof*(γ₁)?f*(γ₁), and γ₁→B U is the 3 universal line boundle. So that we can present a (σ_n), where σ_nis the class of the classifying map of the canonical line boundle overC P ⁿ, in terms of the σ_i’s and chosen generators of Π_★(M U).     

Towards relativistic ECP / DFT description of chemical bonding in E112 compounds: spin-orbit and correlation effects in E112X versus HgX (X=H, Au)

The relativistic effective core potential (RECP) approach combined with the spin-orbit DFT electron correlation treatment was applied to the study of the bonding of eka-mercury (E112) and mercury with hydrogen and gold atoms. Highly accurate small-core shape-consistent RECPs derived from Hartree-Fock-Dirac-Breit atomic calculations with Fermi nuclear model were employed. The accuracy of the DFT correlation treatment was checked by comparing the results in the scalar-relativistic (spin-orbit-free) limit with those of high level scalar-relativistic correlation calculations within the same RECP model. E112H was predicted to be slightly more stable than its lighter homologue (HgH). The E112-Au bond energy is expected to be ca. 25–30 % weaker than that of Hg-Au. The role of correlations and magnetic (spin-dependent) interactions in E112-X and Hg-X (X=H, Au) bonding is discussed. The present computational procedure can be readily applied to much larger systems and seems to be a promising tool for simulating E112 adsorption on metal surfaces.