Approximate dynamic programming for stochastic linear control problems on compact state spaces

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal policies usually cannot be computed, not even for instances of moderate size.     

Estimate of the truncation error of finite volume discretization of the Navier–Stokes equations on colocated grids

A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier–Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two‐dimensional flows, but extension to three‐dimensional cases should not pose problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Radiatively induced neutrino masses and large Higgs-neutrino couplings in the Standard Model with Majorana fields

The Higgs sector of the Standard Model (SM) with one right-handed neutrino per family is systematically analyzed. In a model with intergenerational independent mixings between families, we can account for very light neutrinos acquiring Majorana masses radiatively at the first electroweak loop level. We also find that in such a scenario the Higgs coupling to the light-heavy neutrinos and to the heavy-heavy ones may be remarkably enhanced with significant implications for the production of these heavy neutrinos at high energy colliders.     

Strategic customer behavior in a queueing system with delayed observations

We consider the single-server Markovian queue with infinite waiting space and assume that there exists a certain reward-cost structure that reflects the customers’ desire for service and their dislike for waiting. The system is unobservable for the customers at their arrival instants, but the administrator provides them with periodic announcements of their current positions at rate \(\theta \), so that they may renege if it is preferable for them to do so. The customers are strategic, and their decision problem is whether to join or not the system upon arrival and whether to stay or renege later. Their strategies are specified by a join probability q and a reneging threshold n. We determine the equilibrium strategies \((n_e,q_e)\) and study the socially optimal strategies \((n_\mathrm{soc},q_\mathrm{soc})\). Extensive numerical experiments provide interesting qualitative insight about the model. In particular, the equilibrium throughput of the system is a unimodal function of \(\theta \). Moreover, despite the fact that we have an avoid-the-crowd situation, it is possible that \(q_\mathrm{soc}>q_e\), in contrast to the classical unobservable model.     

The electronic structure of Ti2 and Ti2(+)

The Ti(2) and Ti(2)(+) molecular systems have been studied through multireference variational and single reference coupled-cluster methods coupled with large basis sets. Potential energy curves have been constructed for 30 (Ti(2)) and 2 (Ti(2)(+)) states and the usual spectroscopic parameters have been extracted. The main feature of the potential curves is the existence of van der Waals minima (Ti(2)) around 7 bohr irrespective of the molecular symmetry, and 4s(2)-4s(1) interactions (Ti(2)(+)) around 6 bohr. Numerous avoided crossings lead to stronger covalent bonds emanating from 4s(1)-4s(1) atomic distributions. The X-state of the neutral species is formally a (3)Δ(g) state with the first excited state lying within 1 kcal/mol. The removal of the symmetry defining e(-) leads to the X(2)Σ(g)(+) state of Ti(2)(+).     

Delayed Capital Injections for a Risk Process with Markovian Arrivals

Methodology and Computing in Applied Probability - In this paper we propose a generalisation to the Markov Arrival Process (MAP) risk model, by allowing for a delayed receipt of required capital...     

Experimental study of flame stabilization in low Reynolds and Dean number flows in curved mesoscale ducts

Flame stabilization during non-premixed combustion in curved ducts with a diameter of the order of magnitude of the premixed flame thickness of the reactants was investigated experimentally, since it has been established that this is a configuration with potential advantages in the context of “micro”-combustion. It was shown that, in such “mesoscale” tubes, a stable flame oscillation including extinction/re-ignition phenomena can be established for steady boundary conditions. These oscillations lead, under appropriate conditions, to sound emission in the 50–350 Hz range. This was a mode of stabilization in addition to the “classical” steady flamelet, stabilized through thermal losses to the duct walls at higher values of the Reynolds number. Curvature of the duct was shown to have minimal effect on reactant mixing, which was diffusion-controlled, but significantly affected flame thickness and stabilization. To probe the fuel-oxidizer mixing in the U-shaped, optically accessible tubes, laser induced fluorescence of acetone fuel dopant was used, and the flame structure was studied using OH PLIF. The various stabilization regimes are discussed in terms of the Reynolds and Dean numbers of the tube flow.     

Dielectric relaxation spectroscopy in poly(hydroxyethyl acrylates)/water hydrogels

The electrical and dielectric properties of poly(hydroxyethyl acrylate), PHEA, hydrogels were studied by means of dielectric relaxation spectroscopy in wide ranges of frequencies (5–2 × 10⁹ Hz), temperatures (173–363 K) and water contents (0.065–0.46, g of water per gram of dry material). The secondary dipolar mechanisms (γ and β_sw) and the dc conductivity mechanism were studied in detail by analyzing the dielectric susceptibility data within the complex permittivity formalism, the modulus formalism, and the complex impedance formalism. For both mechanisms molecular mobility was found to increase with increasing temperature or increasing water content (T-f-h superposition principle). The energy parameters and the shape parameters of the response were determined for both mechanisms at several water contents and temperatures. The temperature dependence of dc conductivity was found to change from Vogel-Tamman-Fulcher (VTF) type to Arrhenius type at water contents of ca. 0.30. At water contents lower than about 0.30 the hydrogels are homogeneous whereas at higher water contents a separate water phase appears. In terms of the strong/fragile classification scheme our results suggest that the PHEA hydrogels are fragile systems. ©1995 John Wiley & Sons, Inc.