Korn's inequalities for piecewise vector fields

Korn's inequalities for piecewise vector fields are established. They can be applied to classical nonconforming finite element methods, mortar methods and discontinuous Galerkin methods.

     

Slopes of vector bundles on projective curves and applications to tight closure problems

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from below for the tight closure of a homogeneous -primary ideal in a two-dimensional normal standard-graded algebra in terms of the minimal and the maximal slope of the sheaf of relations for some ideal generators. If moreover this sheaf of relations is semistable, then both degree estimates coincide and we get a vanishing type theorem.

     

Narrow α + <Superscript>28</Superscript>Si elastic-scattering states at high excitation in <Superscript>32</Superscript>S

The excitation function and angular distributions of elastic α-particle scattering on ²⁸Si have been measured in the laboratory energy range 6-28 MeV using a backscattering technique on a thick target, yielding a continuous energy distribution. More than 200 narrow states are observed, with widths in the range ∼ 30-100 keV at excitation energies E ^* = 13-32 MeV. Angular distributions at backward angles were measured, and angular momentum values of more than 83 states have been deduced. The analysis gives spin-parities J ^π, α-partial widths Γ_α and reduced widths of the narrow high-lying resonant states in ³²S. The experimentally observed states display both the negative- and the positive-parity rotational-like sequences with seemingly no parity splitting, a finding which is at variance with most potential-model predictions. The deduced effective moment of inertia indicates a more extended structure than the ground-state configuration. The observed strength of each ℓ-value is analyzed in terms of an underlying split doorway state of Lorentzian form, which yields an interpretation as fragmented rotational α + ²⁸Si states. Received: 26 June 2000 / Accepted: 16 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: kkallman@abo.fi RID="b" ID="b"Present address: Swedish Polytechnic, FIN-65200 Vasa, Finland. Communicated by D. Guerreau     

Cluster states in the neutron excess nucleus 22Ne

High-spin states of the ²²Ne nucleus in the excitation energy range of 15–30 MeV have been studied. The angular correlation method has been used to determine the spins of excited states. A number of new states with high angular momenta—20.0 MeV (9^?), 20.7 MeV (11^?), 21.6 MeV (9^?), 22.2 MeV (12⁺), and 25.0 MeV (9^?)—have been revealed. They are intensely populated in the reaction ¹⁴C(¹²C, α₁)²²Ne* → α₂ + ¹⁸O and correspond to the rotational bands of various structures.     

Experiments and numerical simulations on damage behavior of biaxially loaded specimen

The paper deals with the effect of stress state on damage and failure behavior of isotropic ductile metals. In the continuum damage model the damage behavior of ductile metals is adequately described by a generalized damage condition and an anisotropic damage rule. The damage criterion is based on series of uniaxial experiments with differently notched specimens and corresponding numerical simulations as well as on various numerical calculations on the micro-scale. Different branches of the damage criterion depending on stress triaxiality and Lode parameter are considered. To be able to validate the proposed stress-state-dependent functions new experiments with two-dimensionally loaded specimens have been developed. Corresponding numerical simulations show that these shear-tension and shear-compression tests cover a wide range of stress triaxialities and Lode parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes

We study a class of symmetric discontinuous Galerkin methods on graded meshes. Optimal order error estimates are derived in both the energy norm and the L ₂ norm, and we establish the uniform convergence of V-cycle, F-cycle and W-cycle multigrid algorithms for the resulting discrete problems. Numerical results that confirm the theoretical results are also presented.     

Carbon Nanostructures

An overview of the various carbon structures with characteristic sizes in the nanoscale region is presented, with special attention devoted to the structures and properties of ‘nanodiamond’ and carbon nanotubes. The term ‘nanodiamond’ is used broadly for a variety of diamond-based materials at the nanoscale ranging from single diamond clusters to bulk nanocrystalline films. Only selected properties of carbon nanotubes are discussed, with an aim to summarize the most recent discoveries. Current and potential applications of carbon nanostructures are critically analyzed.     

Nonequilibrium statistical mechanics of dividing cell populations

We present and study a model for the nonequilibrium statistical mechanics of protein distributions in a proliferating cell population. Our model describes how the total protein variation is shaped by two processes: variation in protein production internal to the cells and variation in division and inheritance at the population level. It enables us to assess the contribution of each of these components separately. We find that, even if production is deterministic, cell division can generate a large variation in protein distribution. In this limit we solve exactly a special case and draw an analogy between protein distribution along cell generations and stress distribution in layers of granular material. At the other limit of extremely noisy protein production, we find that the population structure restrains variation and that the details of division do not affect the tail of the distribution.