Using ion implantation to adjust the transition temperature of superconducting films

We summarize a continuing investigation into using ion implantation to alter the transition temperature of superconducting thin films. The primary motivation for the work presented here was to study the feasibility of using magnetic ion doping to replace the bi-layer T_c control process currently used for certain cryogenic detector applications at National Institute for Standards and Technology. The results from work with various ion species implanted into aluminum, molybdenum, titanium and tungsten host films are presented.     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

Modeling and Analysis of a Long Thin Conducting Stripline

A long thin conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e., the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell's equations and assuming that the current on the stripline is a propagating wave in length direction, asymptotic expressions for the fields inside and in the neighbourhood of the stripline are deduced. These expressions are used to model the stripline in the stripline environment, which leads to a boundary-value problem for the electric potential. This problem is solved by two different approaches, leading to integral equations for the current and for an auxiliary function describing the electric potential. A relation between the current and the auxiliary function is deduced, which is used to obtain asymptotic expressions for current and impedance. Results are compared with a numerical solution of the integral equation for the current and with results in literature.     

Interaction of free-surface waves with floating flexible strips

The method developed by the author to derive a set of algebaic equations to solve the interaction of free-surface waves with a single floating rigid or flexible two-dimensional platform with small draft is extended to the case that the platform consists of strips with different constant flexural rigidity and mass. The method is based on the application of Green's theorem, with a specific choice of the Green function to arrive at a differential-integral equation along the platform. This equation can be solved exactly by means of superposition of exponential functions, a standard method to solve a set of linear differential equations. After integration with respect to the space coordinate the residue theorem leads to both the dispersion relation along each individual strip and an algebraic equation for the coefficients. Due to very fast convergence with respect to the number of coefficients taken into account the series are truncated. Depending on the water-depth, in each series three to ten terms are taken into account. Results are shown for a structure consisting of several strips that are tightly connected and for disjoint strips. In the latter case the computation of the water level between the strips is also computed. The water level and the reflection and transmission coefficients are not unknowns in the algebraic equation, but are computed afterwards by means of Green's theorem.     

Modelling of Diffuse Interfaces with Temperature Gradients

The work is devoted to capillary phenomena in miscible liquids under the assumption that they have a constant and the same density. The model consists of the heat equation, diffusion equation, and the Navier-Stokes equations with the Korteweg stress. We study several configurations corresponding to the microgravity experiments planned for the International Space Station. The basic conclusion of the numerical simulations is that transient capillary phenomena in miscible liquids exist and can produce convective flows sufficiently strong to be observed experimentally. In particular, there exists a miscible analogue to the Marangoni convection where the temperature gradient is applied along the transition zone between two fluids. Convection also appears if, instead of the temperature gradient, the case where the width of the transition zone varies in space is considered. Finally, similar to the immiscible case, miscible drops move in a temperature gradient.     

Wave dynamics on a thin-liquid film falling down a heated wall

The dynamics of a thin liquid film falling down a uniformly heated wall is studied. The model introduced by Kalliadasis et al. [J. Fluid Mech. 475 (2003) 377] for the same problem is revisited and its deficiencies, namely the prediction of a critical Reynolds number with 20% error, cured. For the energy equation a high-order Galerkin projection in terms of polynomial test functions is developed. It is shown that not only does this more refined formulation correct the critical Reynolds number, but it also gives, with an appropriate expansion close to criticality, the long-wave theory. Bifurcation diagrams for permanent solitary waves are constructed and compared with the solution branches obtained from different models. It is shown that, in all cases, the long-wave theory exhibits limit points and branch multiplicity, while the other models predict the continuing existence of solitary waves. Time-dependent computations show that the free surface and interfacial temperature approach a train of coherent structures that resemble the infinite-domain stationary solitary pulses.     

Textural Transitions in a Rotating Slab of 3He-A

The operation of a torsional oscillator for detection, of flow-driven textural transitions in, ³He-A is described. The detection technique, tracking the shift of the resonant frequency of the torsional oscillator, allows us to observe textural changes and the presence of vortices in zero magnetic field. It relies on. the anisotropic superfluid density of ³He-A and its change due to reorientation of the Î-texture caused by counterflow.     

Numerical modelling of the propagation of fast landslides using the finite element method

This paper proposes a two‐dimensional (2D) model for the analysis of the propagation of fast landslides involving a fluidized material such as debris and mud flows, flowslides and avalanching flows. The model is based on the Navier–Stokes depth‐integrated equations. To incorporate the effect of steep slopes and centrifugal forces due to the high velocities characterizing the flowslides and the bed curvature, a curvilinear system of reference is used. The corresponding equations of motion are complemented by depth‐averaged constitutive equations and bed friction laws. The resulting set of differential equations are solved using the two‐step Taylor–Galerkin algorithm. This algorithm has been used by the authors to solve hydraulic and dam‐break problems using the finite element method. Owing to the importance of the source term compared to the advection component, the proposed algorithm follows a splitting scheme using a fourth‐order Runge–Kutta method for integrating the friction and slope components. The performance of the overall approach has been checked in a number of examples. The analysis of the results provides insights into the key elements of the model and shows the adequacy of the method to solve real problems where merging and splitting of the flow occur. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.     

Methodologies for the optimal design of parallel manipulators

In this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two different strategies, resulting in two different types of optimization problem are considered. The first strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two specific formulations of the constrained problem are proposed. The first constrained problem simply aims to fit the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well‐conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2‐dof planar parallel manipulator, and the final formulation is also applied to a 3‐dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators. Copyright © 2003 John Wiley & Sons, Ltd.