The use of stokeslets to describe the arbitrary translation of a disk near a plane wall

A previously presented method is extended to describe the fully three-dimensional Stokes flow generated by the translation in any direction of an arbitrarily oriented disk in fluid bounded by a plane wall. The velocity field is represented solely in terms of stokeslet distributions on the disk, modified to take account of the bounding wall according to the century-old idea of Lorentz. Sets of integral equations of the second kind, not all disjoint, are obtained for the Abel transforms in each Fourier mode of the density functions. However, only a few modes need be considered in determining the flow field to order D ^-3, where D is the distance of the disk axis from the wall. Less detail is required to evaluate the drag force and torque experienced by the disk.     

Collective pinning in a film of finite thickness

The theory of collective pinning, which successfully explains the two-dimensional pinning of flux lines in thin superconducting films, is extended to films of finite thicknessd in order to describe the transition from two- to three-dimensional pinning. After short summaries of the collective pinning idea and of the (nonlocal) elastic properties of the flux-line lattice, the displacement correlation function of a weakly pinned flux-line lattice is calculated for a film. The transverse and longitudinal correlation lengths, which determine the correlation volume and the pinning forcej _c B, are obtained. The condition for the dimensional crossover is given.     

Mean stress effect on Gaßner curves interpreted as shifted Wöhler curves and application to smooth and notched geometries

Recently, the authors proposed the simple idea that Gaßner curves can be interpreted as shifted Wöhler curves if the Palmgren‐Miner rule is applied. The idea is extended here to the general case of nonzero mean stress fatigue loading applied to smooth or notched specimens. The mean stress effect has been addressed through the corrections proposed by Smith‐Watson‐Topper and by Walker. In this way, a new expression for the shift factor G has been obtained. Through the application of the theory of the critical distances in its point variant, G is demonstrated to be valid for both smooth and notched geometries. A comparison with the Society of Automotive Engineers (SAE) Keyhole test program data is added to substantiate the findings.     

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

This study considers an efficient method for the estimation of quantiles associated to very small levels of probability (up to O(10⁻⁹)), where the scalar performance function J is complex (eg, output of an expensive-to-run finite element model), under a probability measure that can be recast as a multivariate standard Gaussian law using an isoprobabilistic transformation. A surrogate-based approach (Gaussian Processes) combined with adaptive experimental designs allows to iteratively increase the accuracy of the surrogate while keeping the overall number of J evaluations low. Direct use of Monte-Carlo simulation even on the surrogate model being too expensive, the key idea consists in using an importance sampling method based on an isotropic-centered Gaussian with large standard deviation permitting a cheap estimation of small quantiles based on the surrogate model. Similar to AK-MCS as presented in the work of Schöbi et al., (2016), the surrogate is adaptively refined using a parallel infill criterion of an algorithm suitable for very small failure probability estimation. Additionally, a multi-quantile selection approach is developed, allowing to further exploit high-performance computing architectures. We illustrate the performances of the proposed method on several two to eight-dimensional cases. Accurate results are obtained with less than 100 evaluations of J on the considered benchmark cases.     

IMPROVED TRANSVERSE SHEAR STRESSES IN COMPOSITE FINITE ELEMENTS BASED ON FIRST ORDER SHEAR DEFORMATION THEORY

A method for calculating improved transverse shear stresses in laminated composite plates, which bases on the first-order shear deformation theory is developed. In contrast to many recently established methods, either higher-order lamination theories or layerwise theories, it is easily applicable to finite elements, since only C⁰-continuity is necessary and the numerical effort is low. The basic idea is to calculate the transverse shear stresses directly from the transverse shear forces by neglecting the influence of the membrane forces and assuming two cylindrical bending modes. Shear correction factors are no longer required, since the transverse shear stiffnesses are also provided. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show the superiority of the method against using shear correction factors. Furthermore, results obtained with MSC/NASTRAN, which uses a similar but simplified approach, are surpassed. © 1997 by John Wiley & Sons, Ltd.     

On an SSOR matrix relationship and its consequences

A matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k-cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k-step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k-step one. To show how the idea works the case k = 2 is very briefly discussed.     

Finite block method for transient heat conduction analysis in functionally graded media

Based on the one‐dimensional differential matrix derived from the Lagrange series interpolation, the finite block method is proposed first time to solve both stationary and transient heat conduction problems of anisotropic and functionally graded materials. The main idea is to establish the first order one‐dimensional differential matrix constructed by using Lagrange series with uniformly distributed nodes. Then the higher order of derivative matrix for one‐dimensional problem is obtained. By introducing the mapping technique, a block of quadratic type is transformed from Cartesian coordinate (xyz) to normalised coordinate (ξη?) with 8 seeds or 20 seeds for two or three dimensions. Then the differential matrices in physical domain are determined from that in normalised transformed coordinate system. In addition, the time dependent partial differential equations are analysed in the Laplace transformed domain, and the Durbin inversion method is used to determine the values in time domain. Illustrative two‐dimensional and three‐dimensional numerical examples are given, and comparisons have been made with analytical solutions. Copyright © 2014 John Wiley & Sons, Ltd.     

A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Part 2: Neumann boundary conditions

We present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound‐hard scatterer. We apply this method to the solution of a mock‐up submarine problem, and highlight its computational advantages and intrinsic parallelism. A key component of our method is an original idea for addressing a Neumann boundary condition in the general framework of a fictitious domain method. This idea is applicable to many other linear partial differential equations besides the Helmholtz equation. Copyright © 2003 John Wiley & Sons, Ltd.     

Superconductivity in a Binary Boson-Fermion Mixture with Weak Interaction

A concept describing the origin of the pseudogap phase of high-T _c superconducting cuprates is discussed. Based on the idea about electron-composite boson mixture, existing below some value T _p in cuprates, first, an analytical expression for T _p is obtained. It is shown that T _p depends on interaction parameter responsible for two electron-composite boson transformation, as well on the boson formation energy. Second, the composite boson condensation temperature T _c, determined as a one below which the density of condensed bosons just ceases to be zero, is found. The reason why the behaviors of T _p and T _c in dependence on the interaction parameter may be so different is addressed.     

Adiabatic transfer between cavity modes

Abstract

The idea of counter-intuitive transfer is taken over from atomic systems to a two-mode Jaynes-Cummings model with degenerate mode frequencies. We show that an arbitrary photon state can be transferred between the two modes utilizing a suitable pulse sequence. The method is illustrated by the transfer of pure n-states and coherent states. The numerical analysis of the situation allows us to determine which parameters give adiabatic transfer and the magnitude and character of the corrections. The method is related to earlier work and possible extensions are discussed.     

Complex Gaussian functions expansion method applied to truncated Gaussian beams

An analytical expression for the beam propagation factor (M ² factor) of truncated Gaussian beams was derived by using the complex Gaussian functions expansion method. The reasonability of the approximation of complex Gaussian functions expansion method is studied, and a comparison of this method with the generalised truncated second-order moments method and the asymptotic analysis method is also made. In general, an easy analytical expression for the M ² factor of truncated laser beams can be derived by using the complex Gaussian functions expansion method. The M ² factor obtained by using the complex Gaussian functions expansion method is more consistent with that in practice than that obtained by using two other methods. The analytical results obtained by using the complex Gaussian functions expansion method can be reduced to that for the non-truncated case when the truncation parameter is sufficiently large. Therefore, the complex Gaussian functions expansion method is a suitable approximation method for studying the M ² factor of truncated laser beams.     

Re-entrant lines with unreliable asynchronous machines and finite buffers: performance approximation and bottleneck identification

In this paper we study a re-entrant line with unreliable asynchronous exponential machines and finite buffers. First, an approximation method is presented to estimate the throughput of the re-entrant line. The idea of the approximation is to transform an M-machine re-entrant line into a 2M-machine serial line. Then, a system approach to identify a c-bottleneck based on blockage and starvation information is proposed, where a c-bottleneck machine is the machine whose improvement in machine capacity leads to the largest improvement in system throughput compared with improving all other machines. It is shown that the approximation method results in acceptable accuracy, and the bottleneck identification method can correctly detect the bottlenecks in most cases.     

C2-CONTINUOUS ELEMENTS FOR BOUNDARY ELEMENT ANALYSIS

Overhauser's original idea of linearly blending two sets of quadratic C⁰-continuous basis functions to produce a set of C¹-continuous basis functions is employed by linearly blending two sets of quadratic C¹-continuous basis functions. The result is a set of eight basis functions which are C²-continuous from element to element and can be used for boundary element analysis where post-processing of the solution is required. Solutions to Laplace's equation in simple geometries are used to demonstrate the accuracy of the solutions obtained with the new elements. These new elements also provide more accurate values for the first and second derivatives of the solution in the tangential direction at all points on a smooth boundary and good approximations at corner points. © 1997 by John Wiley & Sons, Ltd.     

Prediction of no-recrystallization temperature by simulation of multi-pass flow stress curves from single-pass curves

In this investigation an algorithm is given to simulate the flow stress curves for multi-pass hot deformation processes simply from the data obtained from single-pass hot torsion test. Using the obtained multi-pass curves the value of no-recrystallization temperature (T _nr) is calculated. This method is examined on a Nb-microalloyed steel. Maximum error in calculation of T _nr with this method and the values obtained from empirical tests was 1.5% which is a very low value. The predicted results are found to be in accord with the experimental data.     

Performance analysis for tandem manufacturing lines under variable structure production control method

In this paper we introduce novel results for the performance of the surplus-based decentralised production control method. The main objective of this production method is to guarantee that the cumulative number of produced products follows the cumulative production demand on the output of any given network. As a starting point of our research a general idea of this method is presented for the case of one manufacturing machine. Then our analysis is extended to a line of N machines. The proposed methodology is reformulated in terms of variable structure control. The production flow process is described by means of difference equations and, in order to analyse the performance, the Lyapunov theory approach is exploited. The results obtained for the production error bounds for each machine in the line and for the buffer content bounds for each intermediate buffer are discussed. Performance and robustness issues of closed-loop flow line models are illustrated by numerical simulations. It is shown that the method can be implemented in enterprise planning tools.     

Characteristics of nanostructure and electrical properties of Ti thin films as a function of substrate temperature and film thickness

Titanium films of different thickness at different substrate temperatures are prepared using PVD method. The nanostructure of these films was obtained using X-ray diffraction (XRD) and AFM, while the thicknesses were measured by means of Rutherford back scattering (RBS) technique. Resistivity, Hall coefficient, concentration of carriers and the mobility in these films are obtained. The results show that, the rutile phase of TiO₂ is formed which is initially amorphous and as the film thickness increases it tends to become textured in (020) direction, which is more pronounced at higher temperatures and possibly transforms to anatase TiO₂ with (112) orientation for thickest films of 224 nm. The conductivity and concentration of carriers increase with thickness, while the Hall coefficient and the mobility decrease. The activation energies in these samples were obtained from the Arrhenius plots of σ and R _H. For thinner films ( eV) and for thickest film (224 nm) a break point is observed at about 500 K, which is consistent with the idea of more processes becoming activated at higher temperatures.     

A Quasi-Boundary Semi-Analytical Approach for Two-Dimensional Backward Heat Conduction Problems

In this article, we propose a semi-analytical method to tackle the two-dimensional backward heat conduction problem (BHCP) by using a quasi-boundary idea. First, the Fourier series expansion technique is employed to calculate the temperature field u(x, y, t) at any time t < T. Second, we consider a direct regularization by adding an extra termau(x, y, 0) to reach a second-kind Fredholm integral equation for u(x, y, 0). The termwise separable property of the kernel function permits us to obtain a closed-form regularized solution. Besides, a strategy to choose the regularization parameter is suggested. When several numerical examples were tested, we find that the proposed scheme is robust and applicable to the two-dimensional BHCP.     

A membership function approach to lot size re-order point inventory problems in fuzzy environments

Inventory models play an important role in logistics and supply chain management for reducing cost and increasing customer satisfaction. This paper develops an approach to derive the fuzzy objective value and decision variables of the fuzzy lot size re-order point inventory problem with parameters being fuzzy numbers and the shortages are backordered with extra cost incurred. Different from the existing studies, the idea is based on Zadeh's extension principle. A pair of mixed integer nonlinear programs (MINLP) parameterised by the possibility level α is formulated to calculate the lower and upper bounds of the minimal total cost per unit time at α, through which the membership function of the minimal total cost per unit time is constructed. At the same time the membership functions of the optimal order quantity and the optimal re-order point are also provided. A numerical example studied by previous studies is solved successfully to demonstrate the validity of the proposed method. Compared with previous studies, the obtained results which precisely and completely conserve the fuzziness of the input information are more informative for finding the best inventory policy since they are expressed by membership functions rather than by crisp ones. Moreover, to provide representative crisp solutions for designing inventory systems, the Yager's ranking index method is adopted to defuzzify the obtained membership functions. The successful extension of inventory models to fuzzy environments permits inventory models to have wider applications in practice.     

An energy method for calculating the stress intensities in orthotropic bimaterial fracture

An energy based numerical method has been developed for extracting stress intensities at the tip of an interface crack bounded by two orthogonal dissimilar materials and subjected to a general state of stress. The method is most suitable for mixed mode delamination fracture studies often observed in brittle matrix composite laminates. After obtaining the near-tip finite element solution for a given laminated geometry, the elastic energy release rate, i.e., J is computed via the stiffness derivative method. The individual orthotropic stress intensities, K _I ^*, K _II ^* are then calculated at a minimum computational expense from further J calculations perturbed by reciprocal stress intensity increments. Results obtained using the Crack Surface Displacement (CSD) method were found to be in good agreement with those obtained using the energy method. Comparisons with theoretical solutions indicate that the energy method can be used accurately even when relatively coarse finite element meshes containing approximately 200 eight noded isoparametric elements are used. The method provides an effective and reliable tool for studying via the method of finite elements delamination phenomena in composite anisotropic laminates.     

Finite cell method

A simple yet effective modification to the standard finite element method is presented in this paper. The basic idea is an extension of a partial differential equation beyond the physical domain of computation up to the boundaries of an embedding domain, which can easier be meshed. If this extension is smooth, the extended solution can be well approximated by high order polynomials. This way, the finite element mesh can be replaced by structured or unstructured cells embedding the domain where classical h- or p-Ansatz functions are defined. An adequate scheme for numerical integration has to be used to differentiate between inside and outside the physical domain, very similar to strategies used in the level set method. In contrast to earlier works, e.g., the extended or the generalized finite element method, no special interpolation function is introduced for enrichment purposes. Nevertheless, when using p-extension, the method shows exponential rate of convergence for smooth problems and good accuracy even in the presence of singularities. The formulation in this paper is applied to linear elasticity problems and examined for 2D cases, although the concepts are generally valid. The first author would like to appreciate the financial support of his stay in Germany, where this research has been carried out, by the Alexander von Humboldt foundation.