Modified Weight Function Research Articles

An immersed moving boundary for fast discrete particle simulation with complex geometry

An immersed moving boundary (IMB) scheme in LBM-DEM is proposed for discrete particle simulation with arbitrarily complex geometry. Momentum exchange between fluid and unresolved particles can be exerted by a modified weighting function with drag force and a new solid operator in IMB, which can describe both particle–fluid interaction and complex geometry, and requires only local information in perspective of solution. Combined with stereolithography (STL) format for describing complex geometry, a GPU-based LBM-DEM-IMB is implemented, and its ability and accuracy for complex geometry from STL model is verified by simulating flow past a stationary sphere. Compared with CFD-DEM in discrete particle simulations of both fluidized bed with immersed tube and aerosol transporting in human nasal, proposed method has much higher efficiency and maintains comparable accuracy in dense and dilute particle–fluid systems with complex geometry, which demonstrates it to be a promising computational strategy for particle–fluid two-phase flows.

Improved high-order high-resolution energy stable weighted essentially non-oscillatory plus scheme for shock/vortex problems

In the present study, a high-order high-resolution energy stable weighted essentially non-oscillatory plus (ESWENO-P) scheme was developed by improving the weighting function in the energy stable weighted essentially non-oscillatory (ESWENO) scheme. First, the weighting function was modified by introducing a new user-defined parameter. Then, the fine-tuning term in the weighted essentially non-oscillatory-Z plus (WENO-ZP) scheme was adopted to the modified weighting function. A parametric study was conducted to determine the value of the user-defined parameter included in the fine-tuning term. To validate the accuracy and the resolution of the present ESWENO-P scheme, well known one- and two-dimensional benchmark flow problems involving shocks and vortices were tested. It was found that, compared to the ESWENO, the present ESWENO-P scheme is more stable near strong discontinuities. It was also observed that, compared to the WENO-ZP, the present ESWENO-P scheme was less sensitive to the user-defined parameter included in the fine-tuning term. Overall, compared to the existing weighted essentially non-oscillatory (WENO) family schemes, the present ESWENO-P scheme consistently resolves flows with high resolution without much computational overhead.

A 3D finite strain viscoelastic model with uncoupled structural and stress relaxations for shape memory polymers

In this paper, a 3D finite strain viscoelastic model with uncoupled structural and stress relaxations is proposed to characterize the thermomechanical behaviors of amorphous shape memory polymers (SMPs). The temperature- and rate-dependent viscoelastic behaviors and stress relaxation are described by the modified Eyring model and nonlinear Adam-Gibbs model based on molecular mechanism. A modified weight function analogous to frozen fraction in phase transition theory is proposed to further improve accuracy of the model. The developed model is implemented with MATLAB to simulate shape recovery experiments of amorphous SMPs under constraints or free in the literature. Good consistency between simulation results and experimental data is obtained.

ВЕКТОРИЗАЦИЯ ТЕКСТА С ИСПОЛЬЗОВАНИЕМ МЕТОДОВ ИНТЕЛЛЕКТУАЛЬНОГО АНАЛИЗА ДАННЫХ

In the text mining tasks, textual representation should be not only efficient but also interpretable,as this enables an understanding of the operational logic underlying the data miningmodels. Traditional text vectorization methods such as TF-IDF and bag-of-words are effective andcharacterized by intuitive interpretability, but suffer from the «curse of dimensionality», and theyare unable to capture the meanings of words. On the other hand, modern distributed methods effectivelycapture the hidden semantics, but they are computationally intensive, time-consuming,and uninterpretable. This article proposes a new text vectorization method called Bag of weightedConcepts BoWC that presents a document according to the concepts’ information it contains. Theproposed method creates concepts by clustering word vectors (i.e. word embedding) then uses thefrequencies of these concept clusters to represent document vectors. To enrich the resulted documentrepresentation, a new modified weighting function is proposed for weighting concepts basedon statistics extracted from word embedding information. The generated vectors are characterizedby interpretability, low dimensionality, high accuracy, and low computational costs when used indata mining tasks. The proposed method has been tested on five different benchmark datasets intwo data mining tasks; document clustering and classification, and compared with several baselines,including Bag-of-words, TF-IDF, Averaged GloVe, Bag-of-Concepts, and VLAC. The resultsindicate that BoWC outperforms most baselines and gives 7 % better accuracy on average

The ∂ Cauchy-Problem on Weakly q-Convex Domains in CPn

Let D be a weakly q-convex domain in the complex projective space ℂPn. In this paper, the (weighted) ∂-Cauchy problem with support conditions in D is studied. Specifically, the modified weight function method is used to study the L2 existence theorem for the ∂-Neumann problem on D. The solutions are used to study function theory on weakly q-convex domains via the ∂-Cauchy problem.

Aluthge transforms of unbounded weighted composition operators in L2‐spaces

AbstractWe describe the Aluthge transform of an unbounded weighted composition operator acting in an L2‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones.

Modified weight function with automatic node generation in element‐free Galerkin method for magnetic field computation

Element-free Galerkin method (EFGM) is one of the numerical methods which is used for solving partial differential equations with moving least squares interpolations. This method is based on finite-element method (FEM) on an integral formulation requires only a set of nodes distributed on the analysis domain for weight function construction. No element connectivity is needed. The objective of this study is to present a modified weight function including automatic node generation for improvement of the EFGM calculation accuracy. Numerical examples show that the effect of the proposed weight function on results accuracy. Verification of improved EFGM simulation results is done by FEM.

The L 2 $$\overline \partial $$ -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds

Let X be a Stein manifold of complex dimension n ⩾ 2 and \(\Omega \Subset X \) be a relatively compact domain with C2 smooth boundary in X. Assume that Ω is a weakly q-pseudoconvex domain in X. The purpose of this paper is to establish sufficient conditions for the closed range of \(\overline \partial \) on Ω. Moreover, we study the \(\overline \partial \)-problem on Ω. Specifically, we use the modified weight function method to study the weighted \(\overline \partial \)-problem with exact support in Ω. Our method relies on the L2-estimates by Hormander (1965) and by Kohn (1973).

New modified weight function for the dissipative force in the DPD method to increase the Schmidt number

To simulate liquid fluid flows with high Schmidt numbers (Sc), one needs to use a modified version of the Dissipative Particle Dynamics (DPD) method. Recently the modifications made by others for the weight function of dissipative forces, enables DPD simulations for Sc, up to 10. In this paper, we introduce a different dissipative force weight function for DPD simulations that allows achieving a solution with higher values of Sc and improving the dynamic characteristics of the simulating fluid. Moreover, by reducing the energy of DPD particles, even higher values of Sc can be achieved. Finally, using the new proposed weight function and , the Sc values can reach up to 200.

Thermal noise of folding mirrors

Current gravitational-wave detectors rely on the use of Michelson interferometers. One crucial limitation of their sensitivity is the thermal noise of their optical components. Thus, for example, fluctuational deformations of the mirror surface are probed by a laser beam being reflected from the mirrors at normal incidence. Thermal noise models are well evolved for that case but mainly restricted to single reflections. In this work, we present the effect of two consecutive reflections under a non-normal incidence onto mirror thermal noise. This situation is inherent to detectors using a geometrical folding scheme such as GEO 600. We revise in detail the conventional direct noise analysis scheme to the situation of non-normal incidence allowing for a modified weighting function of mirror fluctuations. An application of these results to the GEO 600 folding mirror for Brownian, thermoelastic, and thermorefractive noise yields an increase of displacement noise amplitude by 20% for most noise processes. The amplitude of thermoelastic substrate noise is increased by a factor of 4 due to the modified weighting function. Thus, the consideration of the correct weighting scheme can drastically alter the noise predictions and demands special care in any thermal noise design process.

Crack Growth Prediction under Variable Amplitude Loading Considering Elastic-Plastic Stress Field ahead of Crack Tip

Reliable prediction of fatigue life of the structural components under variable amplitude loading requires accurate computation of the residual stresses ahead of crack tip. In present study, a novel method of estimation of linear elastic stress field using concept of fictitious notch rounding is presented. The stress field is later used for evaluation of residual stress distribution. Corrective stress intensity factor is calculated from the residual stress field using modified weight function method. Corrective residual stress intensity factor is used to find the effective maximum stress intensity factor and effective stress intensity range. The values of root radius of aluminium alloys computed using proposed method is found to be closely matching with the values available in literature. Numerical investigation has been carried out to predict remaining life of plate panel with and without considering load interaction effects.

The $$\bar\partial$$ -Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in $$\mathbb{C}P^n$$ with $$n \ge 3$$

In this paper we study the Cauchy–Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the \(\bar\partial\)-Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the \(\bar\partial\)-Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in complex projective spaces of dimension at least three, which removes the smoothness requirement used in an earlier paper of Siu.

Estimation of a Parameter and Its Exact Confidence Interval Following Sequential Sample Size Reestimation Trials

For confirmatory trials of regulatory decision making, it is important that adaptive designs under consideration provide inference with the correct nominal level, as well as unbiased estimates, and confidence intervals for the treatment comparisons in the actual trials. However, naive point estimate and its confidence interval are often biased in adaptive sequential designs. We develop a new procedure for estimation following a test from a sample size reestimation design. The method for obtaining an exact confidence interval and point estimate is based on a general distribution property of a pivot function of the Self-designing group sequential clinical trial by Shen and Fisher (1999, Biometrics55, 190-197). A modified estimate is proposed to explicitly account for futility stopping boundary with reduced bias when block sizes are small. The proposed estimates are shown to be consistent. The computation of the estimates is straightforward. We also provide a modified weight function to improve the power of the test. Extensive simulation studies show that the exact confidence intervals have accurate nominal probability of coverage, and the proposed point estimates are nearly unbiased with practical sample sizes.

Estimation of Weibull parameter with a modified weight function

The Weibull modulus is widely used for estimating the reliability of ceramic components in engineering applications. An improvement in the evaluation of the Weibull modulus is achieved by using an appropriate weight function to the data points while fitting a straight line to the Weibull plot by the least square method. The conventional weight function is a function of the probability of failure. This paper describes an alternate method of obtaining the weight function based on first principles. This modified weight function is a function of the stress at failure rather than probability of failure. Evaluation of the two-parameter Weibull modulus was estimated on simulated strength distribution data with both the weight functions. A comparative analysis indicates that the modified weight function gives a different result than the conventional weight function. The paper also highlights the effect and importance of uncertainties in the measurement of strength on the calculated Weibull modulus.

DETERMINATION OF KI AND KII FOR CURVILINEAR CRACKS UNDER A NON‐UNIFORM BIAXIAL STRESS FIELD

Abstract— Any structural element subjected to a static or alternating biaxial load with variable or random amplitudes may suffer from damage that can be described by fracture mechanics parameters. Brittle fracture conditions, fatigue crack growth rate and direction, as well as corresponding safety margins, are the most important unknowns which have to be predicted.A method is presented for estimating stress intensity factors KI and KII for a curvilinear crack subjected to a non‐uniform biaxial stress field. The method is based on the assumption of an equivalent arc crack, determined separately for each of the real crack tips. The KI and KII values are estimated by means of a modified weight function, called a unitary weight function, evaluated here for the arc crack by using the boundary element method (BEM). According to the principle of superposition any form of non‐uniform stress field may be considered. Accuracy of the method and associated problems of curvilinear crack analysis are also discussed.

Application of a weight function based method to assess partially closed cracks

A new method to study the contact problem in cracks subjected to a strong gradient in the surface direction was presented in a previous work. The method uses the weight function corresponding to the geometry produced by the partial closure of the crack, and is useful to solve the case of an arbitrary monotonically increasing load applied to an infinite cracked plate. In the present work, we study the cases of centre-cracked strips and three-dimensional embedded circular cracks subjected to different load configurations. Weight functions provided by handbooks as well as a geometrically defined weight function are evaluated and used to solve these problems. A modified weight function is presented for the centre-cracked. strip. All results are compared with those obtained using Finite Element and Boundary Element Methods, with good agreement.

Computation of incompressible viscous flows by the third‐order upwind finite element method

AbstractA third‐order upwind finite element scheme is presented for numerical solutions of incompressible viscous flow problems. In order to achieve the third‐order upwind approximation for only the convection term in the Navier‐Stokes equations, a simplified Petrov‐Galerkin formulation in which a modified weighting function is expressed by the sum of a standard weighting function and its second and third spatial derivatives is employed. The mixed method is also employed in the formulation so that a discretization with high‐order accuracy in space is carried out by the use of linear elements. Because a truncation error caused by the third‐order upwind approximation is smaller than that of a first‐order upwind scheme, it is expected that the third‐order upwind scheme will greatly improve the numerical solutions of the Navier‐Stokes equations. Numerical results in one and two dimensions are presented to illustrate the effectiveness of the proposed scheme.

Third-order upwind finite element formulations for incompressible viscous flow problems

A third-order upwind finite element scheme based on the Petrov-Galerkin formulation is presented for highly accurate solutions of convection dominated flows. A new modified weighting function which is expressed by the sum of a standard weighting function and its second and third derivatives is applied to the formulation. The discrete forms for artificial dissipation terms in the upwind scheme can be rewritten by expressions of fourth and fifth spatial derivatives of an unknown function by applying the Taylor-series expansion. The third-order upwinding technique is first applied to the one-dimensional advection-diffusion equation so that the structures of the upwind scheme are explained in detail. Next the upwind scheme is extended to the incompressible Navier-Stokes equations in multidimensions. Numerical results for a driven cavity flow in a two-dimensional square region are presented to demonstrate the effectiveness and applicability of the upwind finite element scheme proposed in this paper.

An enthalpy formulation for phase change problems with a large thermal diffusivity jump across the interface

An enthalpy formulation is proposed in the present investigation for a phase change material (PCM) having a distinct freezing temperature. The latent heat is separated from the sensible heat such that there exists a dependent variable (the sensible heat) that is a continuous function over the entire physical domain. Inside each control volume, the latent heat is rigorously evaluated from the fraction of the liquid phase to achieve an even latent heat evolution. In the dimensionless transformation, the characteristic time is denned in terms of the Stefan number. The coefficients of the unsteady terms thus are always less than unity. This will achieve a good numerical stability for any Stefan number. In addition, this particular transformation makes the present enthalpy formulation applicable to single phase problems if an infinite Stefan number is assigned. To account for a thermal diffusivity jump at the liquid-solid interface, a modified weighting function scheme is developed. Through a few examples, the present enthalpy formulation is seen to produce an accurate and smooth liquid-solid interface for PCM having a distinct freezing point.

The Fourier reconstruction of a head section

The Fourier reconstruction may be viewed simply in the spatial domain as the sum of each line integral times a weighting function of the distance from the line to the point of reconstruction. A modified weighting function simultaneously achieves accuracy, simplicity, low computation time, as well as low sensitivity to noise. Using a simulated phantom, the authors compare the Fourier algorithm and a search algorithm. The search algorithm required 12 iterations to obtain a reconstruction of accuracy and resolution comparable to that of the Fourier reconstruction, and was more sensitive to noise. To speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma.