Midplane-symmetry breaking in the flow between two counter-rotating disks

This paper considers the axisymmetric steady flow driven by exact counter rotation of two co-axial disks of finite radius. At the edges of the rotating disks one of three conditions is (typically) imposed: (i) zero velocity, corresponding to a stationary, impermeable, cylindrical shroud (ii) zero normal velocity and zero tangential fluid traction, corresponding to a (confined) free surface and (iii) an edge constraint that is consistent with a similarity solution of von Kármán form. The similarity solution is valid in an infinite geometry and possesses a pitchfork bifurcation that breaks the midplane symmetry at a critical Reynolds number. In this paper, similar bifurcations of the global (finite-domain) flow are sought and comparisons are made between the resulting bifurcation structure and that found for the similarity solution. The aim is to assess the validity of the nonlinear similarity solutions in finite domains and to explore the sensitivity of the solution structure to edge conditions that are implicitly neglected when assuming a self-similar flow. It is found that, whilst the symmetric similarity solution can be quantitatively useful for a range of boundary conditions, the bifurcated structure of the finite-domain flow is rather different for each boundary condition and bears little resemblance to the self-similar flow.     

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.     

Application of Support Vector Machines in Assessing Conceptual Cost Estimates

Total conceptual cost estimates and the assessment of the quality of these estimates are critical in the early stages of a building construction project. In this study, the support vector machine (SVM) model for assessing the quality of conceptual cost estimates is proposed, and the application of SVM in construction areas is investigated. The results show that the SVM model assessed the quality of conceptual cost estimates slightly more accurately than the discriminant analysis model. This shows that using the SVM has potential in construction areas. In addition, the SVM model can assist clients in their evaluation of the quality of the estimated cost and the probability of exceeding the target cost, and in their decision on whether or not it is necessary to seek a more accurate estimate in the early stages of a project.     

Defining Yield from Bender Element Measurements in Triaxial Stress Probe Experiments

This paper describes the elastic response of a block sample of compressible Chicago glacial clay under a variety of stresses and its relationship with the deformation characteristics at relatively large strains. The elastic shear stiffness was obtained from bender element tests during consolidation and shearing in drained triaxial stress probe tests. An empirical correlation was established based on the elastic shear stiffness in a preyield condition. By comparing the empirical correlation with the measured elastic shear stiffness in the stress region during probing, the changes of elastic shear stiffness were investigated. The departure of elastic shear stiffness from values computed by the empirical relation based on K0 loading directly relates to the yielding characteristics of the clay. The large-scale change of soil structure at yielding alters the well-established relationship between the elastic shear stiffness and stresses in the preyield condition. The mechanical yielding response of clays can be detected based on the systematic analysis of the elastic shear wave velocities.     

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.     

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.