Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Interactions between the oscillations of piezoceramic transducer and the mechanism of as excitation-the generator of the electric current of limited power-supply-are analyzed in this paper In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power as that provided by a dc motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a nonideal problem. In this work, we present certain phenomena as Sommerfeld effect, jump, saturation, and stability, through the influences of the parameters of the governing equations motion. [DOI: 10.1115/1.3007909]

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Quantum spin ladder systems associated with su(2 vertical bar 2)

Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2 \2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second model the addition of extra interactions allows us to impose Heisenberg rung interactions without violating integrability. The existence of a Bethe ansatz solution for both models allows us to investigate the elementary excitations for antiferromagnetic rung couplings. We find that the first model does not show a gap whilst in the second case there is a gap for all positive values of the rung coupling.

On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1

We prove that for any real number p with 1 p less than or equal to n - 1, the map x/\x\ : B-n --> Sn-1 is the unique minimizer of the p-energy functional integral(Bn) \delu\(p) dx among all maps in W-1,W-p (B-n, Sn-1) with boundary value x on phiB(n).

Quantification of carbamazepine, carbamazepine-10,11-epoxide, phenytoin and phenobarbital in plasma samples by stir bar-sorptive extraction and liquid chromatography

A sensitive and reproducible stir bar-sorptive extraction and high-performance liquid chromatography-UV detection (SBSE/HPLC-UV) method for therapeutic drug monitoring of carbamazepine, carbamazepine-10,11-epoxide, phenytoin and phenobarbital in plasma samples is described and compared with a liquid:liquid extraction (LLE/HPLC-UV) method. Important factors in the optimization of SBSE efficiency such as pH, extraction time and desorption conditions (solvents, mode magnetic stir, mode ultrasonic stir, time and number of steps) assured recoveries ranging from 72 to 86%, except for phenytoin (62%). Separation was obtained using a reverse phase C-18 column with UV detection (210 nm). The mobile phase consisted of water: acetonitrile (78:22, v/v). The SBSE/HPLC-UV method was linear over a working range of 0.08-40.0 mu g mL(-1) for carbamazepine, carbamazepine-10,11-epoxide and phenobarbital and 0.125-40.0 mu g mL(-1) for phenytoin, The intra-assay and inter-assay precision and accuracy were studied at three concentrations (1.0, 4.0 and 20.0 mu g mL(-1)). The intra-assay coefficients of variation (CVs) for all compounds were less than 8.8% and all inter-CVs were less than 10%. Limits of quantification were 0.08 mu g mL(-1) for carbamazepine, carbamazepine-10,11-epoxide and phenobarbital and 0.125 mu g mL(-1) for phenytoin. No interference of the drugs normally associated with antiepileptic drugs was observed. Based on figures of merit results, the SBSE/HPLC-UV proved adequate for antiepileptic drugs analyses from therapeutic levels. This method was successfully applied to the analysis of real samples and was as effective as the LLE/HPLC-UV method. (c) 2008 Elsevier B.V. All rights reserved.

Simultaneous analysis of parabens in cosmetic products by stir bar sorptive extraction and liquid chromatography

A sensitive and precise stir bar sorptive extraction (SBSE) combined with LC (SBSE/LC) analysis is described for simultaneous determination of methyl, ethyl, propyl, and butyl parabens in commercial cosmetic products in agreement with the European Union Cosmetics Directive 76/768/EEC. Important factors in the optimization of SB SE efficiency are discussed, such as time and temperature of extraction, pH, and ionic strength of the sample, matrix effects, and liquid desorption conditions by different modes (magnetic stirring, ultrasonic). The LOQs of the SBSE/LC method ranged from 30 to 200 ng/mg, with linear response over a dynamic range, from the LOQ to 2.5 mu g/mg, with a coefficient of determination higher than 0.993. The interday precision of the SBSE/LC method presented a coefficient of variation lower than 5%. The effectiveness of the proposed method was proven for analysis of commercial cosmetic products such as body creams, antiperspirant creams, and sunscreens.

Rifampicin determination in plasma by stir bar-sorptive extraction and liquid chromatography

A sensitive and reproducible stir bar-sorptive extraction and high performance liquid chromatography-UV detection (SBSE/HPLC-UV) method for therapeutic drug monitoring of rifampicin in plasma samples is described and compared with a liquid:liquid extraction (LLE/HPLC-UV) method. This miniaturized method can result in faster analysis, higher sample throughput, lower solvent consumption and less workload per sample while maintaining or even improving sensitivity. Important factors in the optimization of SBSE efficiency such as pH, temperature, extraction time and desorption conditions (solvents, mode magnetic stir, mode ultrasonic stir, time and number of steps) were optimized recoveries ranging from 75 to 80%. Separation was obtained using a reverse phase C(8) column with UV detection (254 nm). The mobile phase consisted of methanol:0.25 N sodium acetate buffer, pH 5.0 (58:42, v/v). The SBSE/HPLC-UV method was linear over a working range of 0.125-50.0 mu g mL(-1). The intra-assay and inter-assay precision and accuracy were studied at three concentrations (1.25, 6.25 and 25.0 mu g mL(-1)). The intra-assay coefficients of variation (CVs) for all compounds were less than 10% and all inter-CVs were less than 10%. Limits of quantification were 0.125 mu g mL(-1). Stability studies showed rifampicin was stable in plasma for 12 h after thawing; the samples were also stable for 24 h after preparation. Based on the figures of merit results, the SBSE/HPLC-UV proved to be adequate to the rifampicin analyses from therapeutic to toxic levels. This method was successfully applied to the analysis of real samples and was as effective as the LLE/HPLC-UV method. (C) 2009 Elsevier B.V. All rights reserved.

Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).

Technical modifications in stabilisers and in bar removal in the Nuss procedure

Pectus excavatum is a congenital deformity that can require surgical treatment. Since Nuss proposed a correction technique, several modifications have been proposed in order to achieve more safety and efficiency in the placement and removal of both bars. Our objective is to describe the technique of placing and removing the bars by proposing three technical modifications: two in bar placement and one in the bar removal. We describe two cases where Nuss bars were placed and one case where the bar was removed as per the technical modification proposed herein. According to the original technique, bar stabilisers. were placed close to the lateral bar edges. We propose a more medial position in order to reduce bar displacement. New stabilisers were designed with central grooves in the posterior surface, which allow better sliding. The technical modification suitable for bar removal was the use of a protective film around the bars to protect the surrounding tissues from the sharp edges, and thereby minimise the risk of injuries. All the proposed modifications were performed without any additional surgical risk or perioperative complication. These three technical modifications can be easily and safety performed, and seem to reduce the risk of bleeding with no additional perioperative complications. (C) 2009 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved.