Synthesis and catalytic performance of CeOCl in Deacon reaction

Surface chlorinated CeO2 is an efficient material for HCl oxidation, which raises the question whether an oxychloride phase could be also active in the same reaction. CeOCl was synthesized by solid state reaction of cerium oxide with anhydrous cerium chloride and tested in HCl oxidation using various feed compositions at 703 K. X-ray diffraction of post-reaction samples revealed that CeOCl is unstable, in both oxygen-rich and -lean conditions. Applying oxygen over-stoichiometric feeds led to complete transformation of CeOCl into CeO2. Considerable HCl conversions were obtained only after this transformation, which confirms the essential role of bulk cerium oxide in this catalytic system

Numerical investigation of an incompressible flow over a backward facing step using a unified fractional step, artificial compressibility and pressure projection (ESAC-PP) method

This study focuses on an incompressible and laminar flow problem behind a backward facing step by employing a recently developed Fractional-Step, Artificial Compressibility and Pressure-Projection (FSAC-PP) method. The FSAC-PP approach unifies Chorin’s fully-explicit Artificial Compressibility (AC) and semiimplicit Fractional-Step Pressure-Projection (FS-PP) methods within the framework of characteristic-based (CB) Godunov-type schemes for solving the incompressible Navier-Stokes equations. The FSAC-PP approach has been originally introduced for low and moderate Reynolds number flows in conjunction with microfluidic and wide range of multiphysics applications. In this work, we demonstrate the applicability of the novel FSAC-PP method to macro-scale separated flows at a moderate Reynolds number. The computational results obtained with the FSAC-PP approach have been compared to the AC method and experimental data to highlight its favorable accuracy and convergence properties for separated flows

Analytic Continuation of Liouville Theory

Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on the sphere. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville's equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include "solutions" of Liouville's equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of "timelike" Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on the sphere can be computed by the original Liouville path integral evaluated on a new integration cycle.Comment: 86 pages plus appendices, 9 figures, minor typos fixed, references added, more discussion of the literature adde

Predicting non-linear flow phenomena through different characteristics-based schemes

The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

A generalised and low-dissipative multi-directional characteristics-based scheme with inclusion of the local Riemann problem investigating incompressible flows without free-surfaces,

In the present study, we develop a generalised Godunov-type multi-directional characteristics-based (MCB) scheme which is applicable to any hyperbolic system for modelling incompressible flows. We further extend the MCB scheme to include the solution of the local Riemann problem which leads to a hybrid mathematical treatment of the system of equations. We employ the proposed scheme to hyperbolic-type incompressible flow solvers and apply it to the Artificial Compressibility (AC) and Fractional-Step, Artificial Compressibility with Pressure Projection (FSAC-PP) method. In this work, we show that the MCB scheme may improve the accuracy and convergence properties over the classical single-directional characteristics-based (SCB) and non-characteristic treatments. The inclusion of a Riemann solver in conjunction with the MCB scheme is capable of reducing the number of iterations up to a factor of 4.7 times compared to a solution when a Riemann solver is not included. Furthermore, we found that both the AC and FSAC-PP method showed similar levels of accuracy while the FSAC-PP method converged up to 5.8 times faster than the AC method for steady state flows. Independent of the characteristics- and Riemann solver-based treatment of all primitive variables, we found that the FSAC-PP method is 7–200 times faster than the AC method per pseudo-time step for unsteady flows. We investigate low- and high-Reynolds number problems for well-established validation benchmark test cases focusing on a flow inside of a lid driven cavity, evolution of the Taylor–Green vortex and forced separated flow over a backward-facing step. In addition to this, comparisons between a central difference scheme with artificial dissipation and a low-dissipative interpolation scheme have been performed. The results show that the latter approach may not provide enough numerical dissipation to develop the flow at high-Reynolds numbers. We found that the inclusion of a Riemann solver is able to overcome this shortcoming. Overall, the proposed generalised Godunov-type MCB scheme provides an accurate numerical treatment with improved convergence properties for hyperbolic-type incompressible flow solvers

Non-renormalization for the Liouville wave function

Using an exact functional method, within the framework of the gradient expansion for the Liouville effective action, we show that the kinetic term for the Liouville field is not renormalized.Comment: 13 pages Latex, no figure

A lecture on the Liouville vertex operators

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.Comment: Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Russia, 2002 v2: Remarks added, typos correcte

Boundary Liouville theory at c=1

The c=1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c=1 limit of unitary minimal models. Here we extend the analysis of the c=1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c=1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c=1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c=1 theory.Comment: 37 pages, 1 figure. Minor error corrected, slight change in result (1.6