Convergence of approximate deconvolution models to the mean Navier–Stokes equations

We consider a 3D Approximate Deconvolution Model ADM which belongs to the class of Large Eddy Simulation (LES) models. We aim at proving that the solution of the ADM converges towards a dissipative solution of the mean Navier–Stokes equations. The study holds for periodic boundary conditions. The convolution filter we first consider is the Helmholtz filter. We next consider generalized convolution filters for which the convergence property still holds.     

Fatigue Crack Nucleation at Σ3(1 1 2) Boundary in a Ferritic Stainless Steel

The effect of a geometrical relationship between a grain boundary (GB) plane and a tensile axis on intergranular fatigue cracking along 3(1 1 2) twin boundaries has been investigated in Fe-30%Cr alloy crystals. Fatigue experiments were carried out on the three kinds of the specimens containing the 3(1 1 2) twin boundary. It was found that the fatigue cracking behavior was sensitive to the geometry of the GB plane. In a specimen where both the GB plane and a slip vector lying in the GB plane in adjacent grains are inclined to the tensile axis at 45°, the fatigue cracks were nucleated preferentially along the twin boundary at a stress amplitude of 170 MPa. The specimen with the GB plane normal to the tensile axis showed that the fatigue crack was initiated from a slip band formed within a constituent grain at a stress amplitude of 300 MPa. When the GB plane was inclined to the tensile axis but the slip vector lying in the GB plane was normal to the tensile axis, development of additional slips formed perpendicular to the GB plane were observed at a specific site of the GB. Initiation of intergranular fatigue cracks at the site was recognized at a stress amplitude of 250 MPa. It can be suggested that the GB plane normal to the tensile axis provides the highest fatigue performance among them. The difference in the cracking property among these specimens could be understood in terms of the effective Schmid factor derived from elastically incompatible stress.     

On list primitive recursion and the complexity of computinginf

We present a primitive recursive programinf_with_lists computing the minimum of two natural numbersn andp (written in unary notation) and using primitive recursion on lists. This program has at first sight the required property of visiting simultaneously its inputs, so it is a counterexample to a theorem showing that such a program cannot be written in the language of primitive recursion on natural numbers, in the more general framework of primitive recursion on term algebras. However, its complexity is at leastinf(n,p)² so it does not implement the algorithm we have in mind to computeinf(n,p).     

A double arity hierarchy theorem for transitive closure logic

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k–1)-ary fragment of partial fixed point logic by all (2k–1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, we show that an extension is possible when we close this logic under congruence.Supported by a grant from the University of Helsinki. This research was initiated while he was a Junior Researcher at the Academy of FinlandThis article was processed by the author using the LATEX style filepljourlm from Springer-Verlag.     

Potential theory of hyperfinite Dirichlet forms

In this paper, we are going to study the capacity theory and exceptionality of hyperfinite Dirichlet forms. We shall introduce positive measures of hyperfinite energy integrals and associated theory. Fukushima's decomposition theorem will be established on the basis of discussing hyperfinite additive functionals and hyperfinite measures. We shall study the properties of internal multiplicative functionals, subordinate semigroups and subprocesses. Moreover, we shall discuss transformation of hyperfinite Dirichlet forms.Research was supported by the National Natural Science Foundation of P.R. China, No. 18901004. The support from the position of Wissenschaftliche Hilfskraft of Ruhr-University Bochum under Prof. Sergio Albeverio is also acknowledged.     

What must and what need not be contained in a graph of uncountable chromatic number?

We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not.     

Comparison of CEPA and CP-MET methods

The known CEPA variants CEPA (v) withv = 0,1,2,3 and two new ones withv = 4, 5 are compared both formally and for various numerical examples with CP-MET. The main conclusions are: 1. In those situations where both CP-MET and the CEPA variants are justified (i.e. for “good” closed shell states) the correlation energies obtained with the 7 different schemes differ very little (by something like ±2%), with CEPA (1) closest to CP-MET (difference usually a fraction of 1%) and CEPA (4) nearly as close; this is rather insensitive to whether one uses canonical or localized orbitals. Even CEPA (3) is not too far from CP-MET, which confirms an earlier suggestion of Kelly. 2. In those cases where one of the 7 schemes fails (e.g. due to near degeneracy as in covalent molecules at large internuclear distances) the other 6 usually fail as well, though CEPA (0) is then somewhat poorer than the other schemes. Then no longer CEPA (1) but rather CEPA (3) is closest to CP-MET and then all schemes converge much better in a localized representation. 3. CEPA (2) usually leads to best agreement with experiment since it simulates to some extent triple substitutions. In none of the studied examples does CP-MET show a significant superiority as compared to the other schemes. Possible improvements to extend the domain of applicability of these methods are discussed.     

The flow due to a rough rotating disk

Von Kármáns problem of a rotating disk in an infinite viscous fluid is extended to the case where the disk surface admits partial slip. The nonlinear similarity equations are integrated accurately for the full range of slip coefficients. The effects of slip are discussed. An existence proof is also given.     

Near Optimal Separation Of Tree-Like And General Resolution

We present the best known separation between tree-like and general resolution, improving on the recent exp(n ) separation of [2]. This is done by constructing a natural family of contradictions, of size n, that have O(n)-size resolution refutations, but only exp((n/log n))- size tree-like refutations. This result implies that the most commonly used automated theorem procedures, which produce tree-like resolution refutations, will perform badly on some inputs, while other simple procedures, that produce general resolution refutations, will have polynomial run-time on these very same inputs. We show, furthermore that the gap we present is nearly optimal. Specifically, if S (S _T ) is the minimal size of a (tree-like) refutation, we prove that S _T = exp(O(S log log S/log S)).* This research was supported by Clore Foundation Doctoral Scholarship. Research supported by NSF Award CCR-0098197 and USA–Israel BSF Grant 97-00188. This research was supported by grant number 69/96 of the Israel Science Foundation, founded by the Israel Academy for Sciences and Humanities.     

On a Problem of Cameron’s on Inexhaustible Graphs

A graph G is inexhaustible if whenever a vertex of G is deleted the remaining graph is isomorphic to G. We address a question of Cameron [6], who asked which countable graphs are inexhaustible. In particular, we prove that there are continuum many countable inexhaustible graphs with properties in common with the infinite random graph, including adjacency properties and universality. Locally finite inexhaustible graphs and forests are investigated, as is a semigroup structure on the class of inexhaustible graphs. We extend a result of [7] on homogeneous inexhaustible graphs to pseudo-homogeneous inexhaustible graphs.The authors gratefully acknowledge support from the Natural Science and Engineering Research Council of Canada (NSERC).