Jump-detection-based estimation in time-varying coefficient models and empirical applications

Time-varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. In some applications, the coefficient curves have singularities, including jump points at some unknown positions, representing structural changes of the related processes. Detection of such singularities is important for understanding the structural changes. In this paper, an alternative jump-detection procedure is proposed based on the first-order and second-order derivatives of the coefficient curves. Based on the detected jump points, a coefficient curve estimation procedure is also proposed, which can preserve the jump structure well when the noise level is small. Further, the implementation of turning parameters is discussed. Under some mild conditions, the asymptotic properties of the proposed estimators are established not only in the continuous regions of coefficient functions, but also in the neighborhoods of the jump points. Finally, we demonstrate, using both simulation and empirical examples, that the proposed methodologies perform well.     

Influence of Stress Singularities on Scaling of Fracture of Metal-Composite Hybrid Structures

It has been recently shown that the nominal structural strength of metal-composite structures depends on the structure size, and such dependence is strongly influenced by the stress singularities. Nevertheless, previous studies only focused on structures that exhibit very strong stress singularities, which are close to the crack-like stress singularity. In the actual engineering designs, due to the mismatch of material properties and complex structural geometries, many metalcomposite structures may contain stress singularities that are much weaker than the crack-like stress singularity. This paper presents a numerical study on the size dependence of scaling of fracture of metal-composite hybrid structures for a wide range of stress singularities. The numerical examples include a series of metalcomposite hybrid beams with a V-notch under three-point bending with different notch angles, which lead to various magnitudes of stress singularities. By assuming that the bimaterial interface is weaker than both metal and composite, we use a mixed-mode cohesive element model to simulate the fracture behavior of these hybrid beams. It is shown that the resulting size effect curves strongly depend on the magnitude of stress singularities. The simulation results agree well with a recently developed energetic-statistical scaling model.     

Expected term bases for generic multivariate Hermite interpolation

The main goal of the paper is to find an effective estimation for the minimal number of points in in general position for which the basis for Hermite interpolation consists of the first ℓ terms (with respect to total degree ordering). As a result we prove that the space of plane curves of degree at most d having singularities of multiplicity ≤ m in general position has the expected dimension if the number of low order singularities (of multiplicity k ≤ 12) is greater then some r(m, k). Additionally, the upper bounds for r(m, k) are given.     

The treatment of singularities in calculation of magnetic field by using integral method

Many papers deal with the calculation of magnetic field using the integral method [1,2]. If the coil consists of straight line and circular arc segments with rectangular cross-sectional winding, the expressions of magnetic field only have analytical terms and one dimensional integrals. Unfortunately, there are some singularities in these expressions when the field points are at some special places in the windings of the coil. These singularities bring on difficulties for the numerical solution of the magnetic field. In this paper, some mathematical treatments to eliminate these singularities are presented which allow accurate numerical solution to the magnetic field.     

Isochromatic fringes in photoelasticity

The structure of the isochromatic fringe pattern in a two-dimensional photoelastic model is investigated with the phase diagram method of the theory of dynamic systems. Isochromatics are interpreted as phase paths (or level curves) of a Hamiltonian system. Possible singularities of the fringe pattern are analyzed.     

Detection of phase singularities with a Shack-Hartmann wavefront sensor

While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical system. Therefore the detection of these phase singularities is an important aspect of strong-scintillation adaptive optics. We investigate the detection of phase singularities with the aid of a Shack-Hartmann wavefront sensor and show that, in spite of some systematic deficiencies inherent to the Shack-Hartmann wavefront sensor, it can be used for the reliable detection of phase singularities, irrespective of their morphologies. We provide full analytical results, together with numerical simulations of the detection process.     

Extension of the method of auxiliary mapping for three‐dimensional elliptic boundary value problems

In this paper, we extend the method of auxiliary mapping (MAM), introduced by Babuška and Oh, to three dimensions so that the extended MAM (3‐D MAM) can effectively handle three‐dimensional elliptic problems containing the singularities caused by the non‐smooth domains. There are three type of singularities caused by non‐smoothness of domains in R ³: the vertex, the edge, and the vertex–edge combined singularities. To deal with the singularities of these types, we present three auxiliary mappings and formulas for the transformed bilinear forms and the transformed linear functionals by these auxiliary mappings. Then we present 3‐D MAM and constructions of the blending‐type elemental mappings for elements containing singularities. Numerical experiments that show the effectiveness of 3‐D MAM are provided. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic caustics in unidirectional fiber-reinforced composites with mode I cracks: Experiment and numerical simulation

The stress singularities of a dynamic crack tip in orthotropic composites were studied through caustics. The parametric equations of the caustic and its initial curve surrounding the dynamic crack tip were derived through the elastic dynamic crack solutions of orthotropic composites and the basic principle of reflective caustics. Theoretical caustics and initial curves for three kinds of orthotropic composites were simulated, and the effects of crack velocity on the caustics and initial curves were analyzed. In comparison with numerical results, the dynamic caustic experiment was performed for dynamic cracks along the material axes in unidirectional, fiber-reinforced composites under drop-hammer, three-point-bend loading.     

应用边界元素法计算文克勒尔地基圆板

本文运用边界元素法的间接法试算了周边自由的文克勒地基园板承受园心集中力、偏心集中力以及均布荷载的挠度,获得了四组挠曲线。对于计算中所遇到的奇异积分是采用分部积分法来消去奇性的。     

Bifurcation and stability of a three‐hinged rod under a conservative load

The bifurcation solutions and their stability of a three‐hinged rod under conservative compressive force are investigated. The equations for the system are non‐linear, and possess some symmetry properties. The symmerty group concepts are employed to exploit these symmetry properties. The symbolic computer software, Mathematica, is used for the analytical and numerical solutions. The loci of codimension‐one singularity are plotted on a two‐dimensional control parameter space. These curves partition the parameter space into regions of qualitatively similar bifurcation diagrams. The bifurcation solutions and their stability at typical points in the parameter diagram, and the perturbation of codimension‐one singularities are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Non-smooth bending and buckling of a strain gradient elastic beam with non-convex stored energy function

Non-smooth strain gradient fields are studied in bending beams, in the context of strain gradient elasticity. It is found that strain fields with continuous curvature, but discontinuous curvature derivatives (evolutes) are possible. The pure bending and buckling problems of a simply supported beam are investigated.     

Singularities of Fourier transforms: A tribute to M. J. Lighthill

Some singular generalised functions of several variables are introduced and their properties described. They are used to support some general theorems to the effect that (a) the singularities of a generalised function are responsible for the behaviour of its Fourier transform at infinity and (b) the behaviour of a generalised function at infinity determines the singularities of its Fourier transform.     

Hierarchical mesh adaptation of 2D quadrilateral elements

In this paper, we present some examples which illustrate the use of adaptive finite element analysis using a new hierarchical refinement algorithm for 2D quadrilateral elements. Projection type a posteriori error estimators based on a global stress smoothing and a simple stress averaging scheme have been used. The algorithm produces well refined meshes for some simple examples which contain stress singularities and stress concentrations. The convergence of the energy norm error has been found to be improved over a previous simple splitting algorithm.     

On Singularities of the Physical Fields at the Edge of a Composite Wedge

We propose analytic procedures capable of evaluation of the orders of power singularities of magnetic fields at the edge of a composite ferromagnetic wedge bordering with a vacuum. The same procedure is used to study the singularities at the edge of a composite piezoceramic wedge. As a result, we present the plots characterizing the dependences of the order of singularities on the wedge angles of the wedges used to form the analyzed composite wedge and the combination of their physical parameters.     

On Special Curves According to Darboux Frame in the Three Dimensional Lorentz Space

In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space. Then, we present some characterizations for these curves and calculate their Darboux invariants. Moreover, we classify TP, TU, PU and TPU-Smarandache curves of a spacelike curve according to the causal character of the vector, curve and surface used in the study. Besides, we give some of differential geometric properties and important relations between that curves. Finally, to demonstrate our theoretical results a computational example is given with graph.     

An iteration method using artificial boundary for some elliptic boundary value problems with singularities

By using an artificial boundary an iteration method is designed to solve some elliptic boundary value problems with singularities. At each step of the iteration the standard finite element method is used to solve the problems in a domain without singularities. It is shown that the iteration method is equivalent to a Schwarz alternating method. Some numerical examples are given, which show the effectiveness of the iteration method. Copyright © 1999 John Wiley & Sons, Ltd.     

Spectral anomalies in focused waves of different Fresnel numbers

Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.     

Conchoidal transform of two plane curves

The conchoid of a plane curve C is constructed using a fixed circle B in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves B and C in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in P ² × P ². We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve C we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.     

Symmetrical frictionless indentation over a uniformly expanding contact region—I. Basic analysis

The study of two-dimensional wave propagation in a half-space due to indentation by a rigid smooth indentor of a general shape at a non-uniform velocity is approached by assuming that the indentor shape and displacement history can be represented by polynomial curves in, respectively, a spatial variable and the time. As a first step symmetric indentation over a contact region expanding at a constant sub-Rayleigh wave speed is considered. Since superposition will yield more general forms attention is confined to polynomials homogeneous of degree $\text{n ? 1}$ with n + 1 terms and arbitrary coefficients. By homogeneous function techniques all the field variables in the half-space for any $\text{n}$ are obtained as single integrals. Conditions for the existence of singularities in the stresses and particle velocities are examined and some general results with bearing on the indentation problem are discussed.     

Silver nanoparticles enhance Pseudomonas aeruginosa PAO1 biofilm detachment

Objectives: Silver nanoparticles (AgNPs) with a size ranging from 7 to 70?nm were synthesized using the ascorbic acid-citrate seed-mediated growth approach at room temperature.

Methods: The 8?nm silver particles were prepared using gallic acid in alkaline conditions and used as seed to prepare AgNPs.

Results: The presence of ascorbic acid and citrate allows the regulation of size and size distribution of the nanoparticles. The increase in free silver ion-to-seed ratio (Ag⁺/Ag⁰) resulted in changes of particle shape from spherical to pseudo-spherical and minor cylindrical shape. Further, a repetitive seeding approach resulted in the formation of pseudo-spherical particles with higher polydispersity index and minor distributions of tetrahedral particles. Citrate-capped AgNPs were stable and did not agglomerate upon centrifugation. The effect of AgNPs on biofilm reduction was evaluated using static culture on 96-well microtiter plates. Results showed that AgNPs with the smallest average diameter were most effective in the reduction of Pseudomonas aeruginosa biofilm colonies, which accounted for 90% of removal.

Conclusion: The biofilm removal activities of the nanoparticles were found to be concentration-independent particularly for the concentration within the range of 80–200?µg/mL.