Energy inconsistency of Galerkin approximationsfor plane Couette flow

For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.     

Quaternionic representation of the 3D elastic and thermoelastic boundary problems

This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis.     

Surface enhanced Raman scattering from mildly roughened surfaces: variation of signal with metal grain size

The intensity of surface enhanced Raman scattering from benzoic acid derivatives on mildly roughened, thermally evaporated Ag films shows a remarkably strong dependence on metal grain size. Large grained (slowly deposited) films give a superior response, by up to a factor of 10, to small grained (quickly deposited) films, with films of intermediate grain size yielding intermediate results. The optical field amplification underlying the enhancement mechanism is due to the excitation of surface plasmon polaritons (SPPs). Since surface roughness characteristics, as determined by STM, remain relatively constant as a function of deposition rate, it is argued that the contrast in Raman scattering is due to differences in elastic grain boundary scattering of SPPs (leading to different degrees of internal SPP damping), rather than differences in the interaction of SPPs with surface inhomogeneities.     

The unitary irreducible representations of the quantum heisenberg algebra

The goal of this work is to describe the irreducible representations of the quantum Heisenberg algebra and the unitary irreducible representation of one of its real forms. The solution of this problem is obtained through the investigation of theleft spectrum of the quantum Heisenberg algebra using the result about spectra of generic algebras of skew differential operators (cf. [R]).     

Local-moment and itinerant antiferromagnetism in the heavy-fermion system Ce(Cu1−xNix)2Ge2

Elastic and inelastic neutron-scattering studies on the system Ce(Cu_1?xNi_x)₂Ge₂ are reported. These measurements are complemented by measurements of the magnetic susceptibility, high-field magnetization, heat capacity, thermal expansion, electrical resistivity and thermopower. The results reveal an interesting T-x phase diagram consisting of two different antiferromagnetic phases for x < 0.2 and 0.2 < x < 0.75, respectively, and a heavy-Fermi-liquid regime at higher Ni concentrations. The experimental results are interpreted in terms of an alloying-induced transition from local-moment to itinerant heavy-fermion magnetism. Fingerprints of this latter phase are a strongly reduced ordered moment and a short incommensurate ordering wave vector, in accord with theoretical predictions. A surprisingly good agreement between theory and experiment is found for x > 0.5. Further experimental evidence for different types of antiferromagnetic ordering derives from a line-shape analysis of the quasielastic neutron-scattering intensity, from magnetization and thermopower experiments.     

Toric cubes

A toric cube is a subset of the standard cube defined by binomial inequalities. These basic semialgebraic sets are precisely the images of standard cubes under monomial maps. We study toric cubes from the perspective of topological combinatorics. Explicit decompositions as CW-complexes are constructed. Their open cells are interiors of toric cubes and their boundaries are subcomplexes. The motivating example of a toric cube is the edge-product space in phylogenetics, and our work generalizes results known for that space.