Skewness, splitting number and vertex deletion of some toroidal meshes

The skewness sk(G) of a graph G = (V, E) is the smallest integer sk(G) >= 0 such that a planar graph can be obtained from G by the removal of sk(C) edges. The splitting number sp(G) of C is the smallest integer sp(G) >= 0 such that a planar graph can be obtained from G by sp(G) vertex splitting operations. The vertex deletion vd(G) of G is the smallest integer vd(G) >= 0 such that a planar graph can be obtained from G by the removal of vd(G) vertices. Regular toroidal meshes are popular topologies for the connection networks of SIMD parallel machines. The best known of these meshes is the rectangular toroidal mesh C(m) x C(n) for which is known the skewness, the splitting number and the vertex deletion. In this work we consider two related families: a triangulation Tc(m) x c(n) of C(m) x C(n) in the torus, and an hexagonal mesh Hc(m) x c(n), the dual of Tc(m) x c(n) in the torus. It is established that sp(Tc(m) x c(n)) = vd(Tc(m) x c(n) = sk(Hc(m) x c(n)) = sp(Hc(m) x c(n)) = vd(Hc(m) x c(n)) = min{m, n} and that sk(Tc(m) x c(n)) = 2 min {m, n}.

Electrodeposition of copper on titanium wires: Taguchi experimental design approach

Electrodeposition of thin copper layer was carried out on titanium wires in acidic sulphate bath. The influence of titanium surface preparation, cathodic current density, copper sulphate and sulphuric acid concentrations, electrical charge density and stirring of the solution on the adhesion of the electrodeposits was studied using the Taguchi statistical method. A L(16) orthogonal array with the six factors of control at two levels each and three interactions was employed. The analysis of variance of the mean adhesion response and signal-to-noise ratio showed the great influence of cathodic current density on adhesion. on the contrary, the other factors as well as the three investigated interactions revealed low or no significant effect. From this study optimized electrolysis conditions were defined. The copper electrocoating improved the electrical conductivity of the titanium wire. This shows that copper electrocoated titanium wires could be employed for both electrical purpose and mechanical reinforcement in superconducting magnets. (C) 2008 Elsevier B.V. All rights reserved.

Superconducting current path and flux line shape in NbTiTa obtained by inter-diffusion process

This investigation presents a comprehensive characterization of magnetic and transport properties of an interesting superconducting wire, Nb-Ti -Ta, obtained through the solid-state diffusion between Nb-12 at.% Ta alloy and pure Ti. The physical properties obtained from magnetic and transport measurements related to the microstructure unambiguously confirmed a previous proposition that the superconducting currents flow in the center of the diffusion layer, which has a steep composition variation. The determination of the critical field also confirmed that the flux line core size is not constant, and in addition it was possible to determine that, in the center of the layer, the flux line core is smaller than at the borders. A possible core shape design is proposed. Among the wires studied, the one that presented the best critical current density was achieved for a diffusion layer with a composition of about Nb-32% Ti-10% Ta, obtained with a heat treatment at 700 degrees C during 120 h, in agreement with previous studies. It was determined that this wire has the higher upper critical field, indicating that the optimization of the superconducting behavior is related to an intrinsic property of the ternary alloy.

Optimization of Heat Treatment Profiles Applied to Nanometric-Scale Nb(3)Sn Wires With Cu-Sn Artificial Pinning Centers

Nb(3)Sn is one of the most used superconducting materials for applications in high magnetic fields. The improvement of the critical current densities (J(c)) is important, and must be analyzed together with the optimization of the flux pinning acting in the material. For Nb(3)Sn, it is known that the grain boundaries are the most effective pinning centers. However, the introduction of artificial pinning centers (APCs) with different superconducting properties has been proved to be beneficial for J(c). As these APCs are normally in the nanometric-scale, the conventional heat treatment profiles used for Nb(3)Sn wires cannot be directly applied, leading to excessive grain growth and/or increase of the APCs cross sections. In this work, the heat treatment profiles for Nb(3)Sn superconductor wires with Cu(Sn) artificial pinning centers in nanometric-scale were analyzed in an attempt to improve J(c) . It is described a methodology to optimize the heat treatment profiles in respect to diffusion, reaction and formation of the superconducting phases. Microstructural, transport and magnetic characterization were performed in an attempt to find the pinning mechanisms acting in the samples. It was concluded that the maximum current densities were found when normal phases (due to the introduction of the APCs) are acting as main pinning centers in the global behavior of the Nb(3)Sn superconducting wire.

Electrical and Magnetic Characterization of BSCCO and YBCO HTS Tapes for Fault Current Limiter Application

Several high temperature superconductor (HTS) tapes have been developed since the late eighties. Due to the new techniques applied for their production, HTS tapes are becoming feasible and practical for many applications. In this work, we present the test results of five commercial HTS tapes from the BSCCO and YBCO families (short samples of 200 mm). We have measured and analyzed their intrinsic and extrinsic properties and compared their behaviors for fault current limiter (FCL) applications. Electrical measurements were performed to determine the critical current and the n value through the V-I relationship under DC and AC magnetic fields. The resistance per unit length was determined as a function of temperature. The magnetic characteristics were analyzed through susceptibility curves as a function of temperature. As transport current generates a magnetic field surrounding the HTS material, the magnetic measurements indicate the magnetic field supported by the tapes under a peak current 1.5 times higher than the critical current, I(c). By pulsed current tests the recovery time and the energy/volume during a current fault were also analyzed. These results are in agreement with the data found in the literature giving the most appropriate performance conductor for a FCL device (I(peak) = 4 kA) to be used in a 220 V-60 Hz grid.

Heat treatment influence on the superconducting properties of nanometric-scale Nb(3)Sn wires with Cu-Sn artificial pinning centers

Since the discovery of Nb(3)Sn superconductors many efforts have been expended to improve the transport properties in these materials. In this work, the heat treatment profiles for Nb(3)Sn superconductor wires with Cu(Sn) artificial pinning centers (APCs) with nanometric-scale sizes were analyzed in an attempt to improve the critical current densities and upper critical magnetic field. The methodology to optimize the heat treatment profiles in respect to the diffusion, reaction and formation of the superconducting phases is described. Microstructural characterization, transport and magnetic measurements were performed in an attempt to relate the microstructure to the pinning mechanisms acting in the samples. It was concluded that the maximum current densities occur due to normal phases (APCs) that act as the main pinning centers in the global behavior of the Nb(3)Sn superconducting wire. The APC technique was shown to be very powerful because it permitted mixing of the pinning mechanism. This achievement was not possible in other studies in Nb(3)Sn wires reported up to now.

Toughened ZrO2 ceramics sintered with a La2O3-rich glass as additive

In this study, the influence of the glass addition and sintering parameters on the densification and mechanical properties of tetragonal zirconia polycrystals (3Y-TZP) ceramics were evaluated. High-purity tetragonal ZrO2 powder and La2O3-rich glass were used as starting powders. Two compositions based on ZrO2 and containing 5wt.% and 10wt.% of La2O3-rich glass were studied in this work. The starting powders were mixed/milled by planetary milling, dried at 90 degrees C for 24 h, sieved through a 60 mesh screen and uniaxially cold pressed under 80 MPa. The samples were sintered in air at 1200 degrees C, 1300 degrees C, 1400 degrees C for 60 min and at 1450 degrees C for 120 min, with heating and cooling rates of 10 degrees C/min. Sintered samples were characterized by relative density, X-ray diffraction (XRD) and scanningelectron microscopy (SEM). Hardness and fracture toughness were obtained by Vickers indentation method. Dense sintered samples were obtained for all conditions. Furthermore, only tetragonal-ZrO2 was identified as crystalline phase in sintered samples, independently of the conditions studied. Samples sintered at 1300 degrees C for 60 min presented the optimal mechanical properties with hardness and fracture toughness values near to 12 GPa and 8.5 MPa m(1/2) respectively. (c) 2007 Elsevier B.V, All rights reserved.

Lightweight composite concrete produced with water treatment sludge and sawdust: Thermal properties and potential application

The main objective of this study was to evaluate the potential application of a lightweight concrete produced with lightweight coarse aggregate made of the water treatment sludge and sawdust (lightweight composite), by determining the thermal properties and possible environmental impact of future residue of this concrete. Two types of concrete were prepared: concrete produced with the lightweight composite dosed with cement/sand/composite/water in a mass ratio of 1:2.5:0.67:0.6 and conventional concrete dosed with cement/sand/crushed stone/water in a mass ratio of 1:4.8:5.8:0.8. The thermal properties were determined by the hot wire parallel technique. The possible environmental impact was measured using the procedures and guidelines of the Brazilian Association of Technical Standards - ABNT. The concrete produced with the lightweight composite presented a 23% lower thermal conductivity than the conventional concrete. The concrete produced with the lightweight composite presented a set of thermal properties suitable for the application of this concrete in non-structural sealing elements. The concentration of aluminum in the solubilized extract of the concrete produced with the lightweight composite was much lower than the concentration of aluminum in the water treatment sludge, confirming the possible reduction of environmental impact of this composite for use in concrete. (C) 2010 Elsevier Ltd. All rights reserved.

Thermal diffusivity of polymers by modified angstrom method

The nature of the molecular structure of plastics makes the properties of such materials markedly temperature dependent. In addition, the continuous increase in the utilization of polymeric materials in many specific applications has demanded knowledge of their physical properties, both during their processing as raw material, as well as over the working temperature range of the final polymer product. Thermal conductivity, thermal diffusivity and specific heat, namely the thermal properties, are the three most important physical properties of a material that are needed for heat transfer calculations. Recently, among several different methods for the determination of the thermal diffusivity and thermal conductivity, transient techniques have become the preferable way for measuring thermal properties of materials. In this work, a very simple and low cost variation of the well known Angstrom method is employed in the experimental determination of the thermal diffusivity of some selected polymers. Cylindrical shaped samples 3 cm diameter and 7 cm high were prepared by cutting from long cylindrical commercial bars. The reproducibility is very good, and the results obtained were checked against results obtained by the hot wire technique, laser flash technique, and when possible, they were also compared with data found in the literature. Thermal conductivity may be then derived from the thermal diffusivity with the knowledge of the bulk density and the specific heat, easily obtained by differential scanning calorimetry. (C) 2009 Elsevier Ltd. All rights reserved.

A simple method for non-linear analysis of steel fiber reinforced concrete

This paper proposes a physical non-linear formulation to deal with steel fiber reinforced concrete by the finite element method. The proposed formulation allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced in the pre-existent finite element numerical system to consider any distribution or quantity of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic of the formulation is the reduced work required by the user to introduce reinforcements, avoiding ""rebar"" elements, node by node geometrical definitions or even complex mesh generation. Bounded connection between long fibers and continuum is considered, for short fibers a simplified approach is proposed to consider splitting. Non-associative plasticity is adopted for the continuum and one dimensional plasticity is adopted to model fibers. Examples are presented in order to show the capabilities of the formulation.

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

A numerical model for the description of the nonlinear behaviour of multi-leaf masonry walls

A nonlinear finite element model was developed to simulate the nonlinear response of three-leaf masonry specimens, which were subjected to laboratory tests with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls up to failure. The specimens consisted of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. Different loading conditions, typologies of the collar joints, and stone types were taken into account. The constitutive law implemented in the model is characterized by a damage tensor, which allows the damage-induced anisotropy accompanying the cracking process to be described. To follow the post-peak behaviour of the specimens with sufficient accuracy it was necessary to make the damage model non-local, to avoid mesh-dependency effects related to the strain-softening behaviour of the material. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases. (c) 2007 Elsevier Ltd. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Experimental study of a Tollmien-Schlichting wave interacting with a shallow 3D roughness element

The paper is devoted to an experimental study of the effect of a shallow 3D roughness element on the evolution of a 2D Tollmien-Schlichting wave in a Blasius boundary layer. The experiments were carried out under controlled disturbance conditions on an airfoil section which could provide a long run with zero pressure gradient flow. A pneumatically driven slit source was used to introduce the Tollmien-Schilichting wave upstream of the lower branch of the neutral stability curve. A few wavelengths downstream, the T-S wave interacts with a cylindrical roughness element. The height of the roughness was slowly oscillating in time, which allows a continuous measurement of the T-S wave response downstream the roughness. The oscillation frequency was approximately 1500 times lower than the frequency of the studied Tollmien-Schlichting wave and therefore, behaved as a steady roughness with respect to the T-S wave. Hot wire anemometry was used to measure wall normal profiles and spanwise scans close to the maximum of the eigenfunction of the T-S wave. The oscillation of the roughness and the synchronization of all-equipments permitted the use of ensemble average techniques. Two different amplitudes of T-S waves with a non-dimensional frequency of F120E-06 were studied. They show a strong amplification of the disturbances in a small spanwise wave number range. The analysis of the wall normal T-S profiles suggests the growth of oblique modes.