A moving mesh algorithm for aero‐thermo‐mechanical modelling in turbomachinery

This paper describes the development of a mesh deformation method used for aero‐thermo‐mechanical coupling of turbo‐engine components. The method is based on the nonlinear solution of an elastic medium analogy, solved using finite element discretisation and modified to let the boundary nodes be free to slide over the deflected surfaces. This sliding technique relies on a B‐spline reconstruction of the moving boundary and increases the robustness of the method in situations where the boundary deflection field presents significant gradients or large relative motion between two distinct boundaries. The performance of the method is illustrated with the application to an interstage cavity of a turbine assembly, subjected to the deformations computed by a coupled thermo‐mechanical analysis of the engine component. Copyright © 2011 John Wiley & Sons, Ltd.     

Kinetic studies of laser-induced synthesis of thin vanadium pentoxide films

The kinetics of Ar⁺ laser-induced oxidation of 100 nm thick vanadium films on glass substrates is followed by measuring time-dependent changes in reflected and transmitted intensity of a He-Ne probe beam. The growth rate of the vanadium pentoxide layer increases with increasing laser powerP as = ₀ exp(-a/P). At power densities above kW/cm² vanadium pentoxide crystallizes from the melt.     

Laser investigations at 269 nm for XeF(D-X) in Ne crystals

From line narrowing in amplified spontaneous emission at the D-X transition (269nm) of XeF in solid Ne a gain coefficient of 3.4 cm^–1 has been derived and ground-state losses of 2.8 cm^–1 have been determined by variation of the absorption length. A dielectric laser cavity has been optimized with the reflectivities R₁=100% and R₂=70% for 1 cm long crystals; laser action has been achieved.     

Lie-admissible structures on Witt type algebras

In this paper we study Lie-admissible structures on Witt type algebras. Witt type algebras are Γ$\Gamma$-graded Lie algebras (where Γ$\Gamma$ is an abelian group) which generalize the Witt algebra. We give all third power-associative and flexible Lie-admissible structures on these algebras. In particular we generalize some results on the Witt algebra. After describing the second scalar cohomology group of Witt type algebras, we investigate third power-associative and flexible Lie-admissible structures on the central extension of some Witt type algebras. Finally we study a left-symmetric structure induced by a symplectic form for some Witt type algebras.     

Integrable Hamiltonian systems related to the Hilbert–Schmidt ideal

By the application of the coinduction method as well as the Magri method to the ideal of real Hilbert–Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on Banach Lie–Poisson spaces which consist of such types of operators. We also discuss their algebraic and analytic properties and solve them in dimensions, N=2,3,4$N=2,3,4$.     

Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is isomonodromic if and only if the residue matrices satisfy the Schlesinger system with respect to the parameter. Without the non-resonance condition this result fails: there exist non-Schlesinger isomonodromic deformations. In the present article we introduce the class of the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal deformation is also an isomonodromic one. In general, the class of the isomonodromic deformations is much richer than the class of the isoprincipal deformations, but in the non-resonant case these classes coincide. We prove that a deformation is isoprincipal if and only if the residue matrices satisfy the Schlesinger system. This theorem holds in the general case, without any assumptions on the spectra of the residue matrices of the deformation. An explicit example illustrating isomonodromic deformations, which are neither isoprincipal nor meromorphic with respect to the parameter, is also given.The research of Victor Katsnelson was supported by the Minerva Foundation.     

The design of the main accelerator for a pulsed positron beam

The pulsed positron beam at the Helsinki University of Technology is designed for the end energy of 3-30 keV and grounded target. This is achieved with a constant voltage acceleration followed by an adjustable deceleration. In the design of this accelerator-decelerator the possibility for electrical breakdowns and partial discharges must be eliminated.For designing the electrode and insulator structures for accelerator-decelerator configuration electric field simulations were carried out with the finite element analysis program. In this paper we present the design of the accelerator-decelerator and the results of the electric field simulations. The results of high voltage tests will also be presented and compared with the simulations.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

The Bogoliubov inner product in quantum statistics

A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relative entropy functional. The basic geometrical quantities, including sectional curvatures, are computed for a two-level quantum system. It is found that the real density matrices form a totally geodesic submanifold and the von Neumann entropy is a monotone function of the scalar curvature. Furthermore, we establish information inequalities extending the Cramér-Rao inequality of classical statistics. These are based on a very general new form of the logarithmic derivative.This work was supported by the Hungarian National Foundation for Scientific Research, grant No. 1900. Authors' e-mail addresses are: H1128PET@ella.hu and TOTH@zodiac.rutgers.edu.