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...     

Structure determination of oligomeric alkannin and shikonin derivatives

Monomeric alkannin and shikonin (A/S) are potent pharmaceutical substances with a wide spectrum of biological activity and comprise the active ingredients for several pharmaceutical preparations. Therefore, the determination of the impurities, degradation products or byproducts in alkannin and shikonin samples is of great importance. Oligomeric alkannin and shikonin are formed during biosynthesis of these bioactive secondary metabolites in Boraginaceaous root plants, during tissue culture production of A/S, during alkaline hydrolysis of A/S esters and also thermal treatment of A/S. In the present study, a dimeric alkannin/shikonin compound was isolated by size exclusion chromatography from alkannin and shikonin commercial samples and its structure was determined by one- and two-dimensional NMR spectroscopy. The structure of the most abundant oligomeric species in these samples, a dimeric naphthoquinone, was established for the fi rst time, indicating that coupling of the side chain of one naphthoquinone unit with the aromatic ring of a second naphthoquinone leads to dimer formation. This type of coupling allows further oligomerization by leaving one isohexenyl side chain available at the second monomer unit.     

Mathematical Models for Studying the Value of Motivational Leadership in Teams

Mathematical models are presented for studying the value of leadership in a team where the members interact with each other. The models are based on a leader’s role of motivating each team member to perform closer to his/her maximum ability. These models include controllable parameters whose values reflect the amount of task interdependence among the workers as well as the motivational skill and variability in the skill of the leader. Confirming results—such as the fact that the skill level of the leader is a critical factor in the expected performance of the team—establish credibility in the models. Mathematical analysis and computer simulations are used to provide new managerial insights into the value of the leader—such as the fact that the skill of the leader can be more important than controlling the amount of interdependence among the team members and that having a choice of multiple leaders with no particular motivating skill is beneficial to the performance of small teams but not to large teams.Daniel Solow received a B.S. in Mathematics from Carnegie-Mellon, an M.S. in Operations Research from the University of California at Berkeley, and a Ph. D. in Operations Research from Stanford University. He has been a professor at Case Western Reserve University since 1978. His research interests include complex systems, discrete, linear, and nonlinear optimization. He has also developed systematic methods for teaching mathematical proofs, computer programming, and operations research.Sandy Kristin Piderit is an assistant professor of organizational behavior at the Weatherhead School of Management at Case Western Reserve University, and earned her Ph.D. from the University of Michigan. She studies the roles of relationships among coworkers on their performance and satisfaction with their work environments, and has published studies in the Academy of Management Review, the Journal of Management Studies, and Management Science.Apostolos Burnetas received a Diploma in Electrical Engineering from National Technical University in Athens, Greece, and an M.B.A. and Ph.D. in Operations Research from Rutgers University. He has been at the Department of Operations at Case Western Reserve University and is currently an Associate Professor at the Department of Mathematics at the University of Athens. His research interests include stochastic models and optimization, complex systems, and applications in queueing systems, supply chain and the interface of operations with finance.Chartchai Leenawong received a B.S. in Mathematics from Chulalongkorn University in Bangkok, an M.S. in Computer Science from the Asian Institute of Technology in Bangkok, and a Ph.D. in Operations Research from Case Western Reserve University. His research interests include mathematical modeling of complex systems as applied to business organizations. He has been a professor at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand since 2002.     

Symmetry-improved CJT effective action

The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2)$\mathbb{O}(2)$ scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2)$\mathbb{O}(2)$ is massless and the phase transition is a second-order one, already in the Hartree–Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree–Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.