The effect of solidification time and heat treatment on the fatigue properties of a cast 319 aluminum alloy

Solidification time and heat treatment are known to have a large effect on the microstructure of cast aluminum alloys. This study was conducted to quantify how the fatigue properties of a 319-type aluminum alloy are affected by solidification time and heat treatment. Both porosity-containing (non-hot isostatically pressed (HIP)) and porosity-free (HIP) samples in the T6 (“peak aged”) or T7 (“overaged”) heattreated conditions were tested. As the solidification time increased, the average initiating pore diameter increased and stress-controlled fatigue life decreased. Heat treatment was observed to have a large effect on fatigue properties of the HIP samples. However, in the non-HIP fatigue samples, heat treatment did not significantly change the fatigue life or fatigue strength of the cast 319-type alloy. The absence of an influence of heat treatment on fatigue response is attributed to the predominance of the microporosity in fatigue crack initiation in cast aluminum.     

Analytical results for the plectonemic response of supercoiled DNA

The DNA molecule is modeled as an elastic rod with bending and twisting rigidities, subjected to external tension and twist applied at one end, the other end being clamped. We study the plectonemic equilibrium of such a rod, taking into account the impenetrability constraint. Numerical solutions of this boundary value problem have previously shown that purely elastic models can reproduce the supercoiling response of the DNA molecule. Using a variational approach, we derive analytical formulae for the elastic response of the filament, and extend former numerical results.     

Influence of Cu<Superscript>2+</Superscript> ions on structural and magnetic properties of NiZn ferrites

The paper is devoted to the preparation of NiZn ferrite with small substitutions of copper by means of ceramic technology. The influence of small Cu substitution on the microstructural and magnetic properties of NiZn ferrites have been analysed by means of various experimental methods and interpreted from the point of view of preparation technology optimisation and possible applications of such materials. A strong correlation between the substituent content and resulting properties has been observed, thus allowing preparation of material with the properties tailored for any particular application.     

Algorithms in the W-Hierarchy

We show new upper bounds for problems in the W-hierarchy of fixed-parameter complexity. A crucial ingredient of our proofs is an extension to the W-RAM model, which permits more-powerful operations but remains equivalent to the original. We use the extended model to give new upper bounds for Subsetsum, Maximum Irredundant Set, and various problems concerning intersection of finite-state machines.     

The Computational Complexity of One-Dimensional Sandpiles

We prove that the one-dimensional sandpile prediction problem is in LOGDCFL, a subset of AC¹. The previously best known upper bound on the ACⁱ-scale was AC². Furthermore, we prove that the one-dimensional sandpile prediction problem is hard for TC⁰ and thus not in AC^1-ε for any constant ε > 0.     

Polynomial-Space Decidable Membership Problems for Recurrent Systems over Sets of Natural Numbers

A finite recurrent system over sets of natural numbers of dimension n is a pair composed of n n-ary functions over sets of natural numbers and an n-tuple of singleton sets of natural numbers. Every function is applied to the entries of the tuple and computes a set of natural numbers, that may also be empty. The results are composed into another tuple, and the process is started anew. Thus, a finite recurrent system defines an infinite sequence of n-tuples containing sets of natural numbers. The last entry of a generated n-tuple is called the output of a step, and the union of the output sets of all steps is the set defined by the finite recurrent system. Membership problems ask whether a given number is in a specified output set or in some output set. We study membership problems for special finite recurrent systems, whose functions are built from the set operations union, intersection and complementation and the arithmetical operations addition and multiplication. Sum and product of two sets of natural numbers are defined elementwise. We restrict the set of operations from which functions are built and determine the impact on the complexity of the membership problems. We focus on PSPACE-decidable membership problems and show completeness results for the complexity classes NL, NP and PSPACE.     

Dynamic Complexity Theory Revisited

Dynamic complexity investigates the required effort to maintain knowledge about a property of a structure under changing operations. This article introduces a refined notion of dynamic problems which takes the initial structure into account. It develops the basic structural complexity notions accordingly. It also shows that the dynamic version of the LOGCFL-complete problem D₂LREACH(acyclic) can be maintained with first-order updates.     

Truthful Approximation Mechanisms for Scheduling Selfish Related Machines

We consider the problem of scheduling jobs on related machines owned by selfish agents. We provide a 5-approximation deterministic truthful mechanism, the first deterministic truthful result for the problem. Previously, Archer and Tardos showed a 2-approximation randomized mechanism which is truthful in expectation only (a weaker notion of truthfulness). In case the number of machines is constant, we provide a deterministic Fully Polynomial-Time Approximation Scheme (FPTAS) and a suitable payment scheme that yields a truthful mechanism for the problem. This result, which is based on converting FPTAS to monotone FPTAS, improves a previous result of Auletta et al., who showed a (4 + ε)-approximation truthful mechanism.