Integral Domain Research Articles

An improved impermeable solid boundary scheme for Meshless Local Petrov–Galerkin method

Meshless methods have become an essential numerical tool for simulating a wide range of flow–structure interaction problems. However, the way by which the impermeable solid boundary condition is implemented can significantly affect the accuracy of the results and computational cost. This paper develops an improved boundary scheme through a weak formulation for the boundary particles based on Pressure Poisson’s Equation (PPE). In this scheme, the wall boundary particles simultaneously satisfy the PPE in the local integration domain by adopting the Meshless Local Petrov–Galerkin method with the Rankine source solution (MLPG_R) integration scheme (Ma, 2005b) and the Neumann boundary condition, i.e., normal pressure gradient condition, on the wall boundary which truncates the local integration domain. The new weak formulation vanishes the derivatives of the unknown pressure at wall particles and is discretized in the truncated support domain without extra artificial treatment. This improved boundary scheme is validated by analytical solutions, numerical benchmarks, and experimental data in the cases of patch tests, lid-driven cavity, flow over a cylinder and monochromic wave generation. Second-order convergent rate is achieved even for disordered particle distributions. The results show higher accuracy in pressure and velocity, especially near the boundary, compared to the existing boundary treatment methods that directly discretize the pressure Neumann boundary condition.

On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua

In the theory of second-gradient continua, the internal virtual work functional can be considered as a second-order distribution in which the virtual displacements take the role of test functions. In its easiest representation, the internal virtual work functional is represented as a volume integral over a subset of the three-dimensional Euclidean vector space and involves first and second derivatives of the virtual displacements. In this paper, we show by an iterative integration by parts procedure how an alternative representation of such a functional can be obtained when the integration domain is a subset that contains also edges and wedges. Since this procedure strongly relies on the divergence theorem for submanifolds of a Euclidean vector space, it is a main goal to derive this divergence theorem for submanifolds starting from Stokes’ theorem for manifolds. To that end, results from Riemannian geometry are gathered and applied to the submanifold case.

Performance analysis of cognitive hybrid radio frequency and free space optical cooperative networks

This paper studies the exact performance of hybrid radio frequency and free space optical cooperative amplify and forward communication networks in a cognitive radio environment, where secondary users cannot transmit signals at any power level since the existence of the primary users restrict the behavior of the secondary users within an acceptable and reasonable range. In particular, a secondary relay station connects a destination through a free space optical link, whose random characteristics follows a widely used gamma–gamma fading distribution with non zero pointing error to characterize the assignable effects of atmospheric turbulence. Different from the traditional analysis methods in probability theory based on cumulative distribution function or outage probability, the complicated integral domain division is avoided by virtue of the moment generating function of reciprocal signal to noise ratio. Under the maximum interference level constraint of the primary user, exact closed form expressions of moments of signal to noise ratio, ergodic capacity, higher order statistics of the capacity, and average bit error probability are derived naturally. Finally, simulation results are provided to flawlessly demonstrate the theoretical analysis.

Experimental Comparisons of Clustering Approaches for Data Representation

Clustering approaches are extensively used by many areas such as IR, Data Integration, Document Classification, Web Mining, Query Processing, and many other domains and disciplines. Nowadays, much literature describes clustering algorithms on multivariate data sets. However, there is limited literature that presented them with exhaustive and extensive theoretical analysis as well as experimental comparisons. This experimental survey paper deals with the basic principle, and techniques used, including important characteristics, application areas, run-time performance, internal, external, and stability validity of cluster quality, etc., on five different data sets of eleven clustering algorithms. This paper analyses how these algorithms behave with five different multivariate data sets in data representation. To answer this question, we compared the efficiency of eleven clustering approaches on five different data sets using three validity metrics-internal, external, and stability and found the optimal score to know the feasible solution of each algorithm. In addition, we have also included four popular and modern clustering algorithms with only their theoretical discussion. Our experimental results for only traditional clustering algorithms showed that different algorithms performed different behavior on different data sets in terms of running time (speed), accuracy and, the size of data set. This study emphasized the need for more adaptive algorithms and a deliberate balance between the running time and accuracy with their theoretical as well as implementation aspects.

Solving Fredholm Integral Equations Using Deep Learning.

The aim of this paper is to provide a deep learning based method that can solve high-dimensional Fredholm integral equations. A deep residual neural network is constructed at a fixed number of collocation points selected randomly in the integration domain. The loss function of the deep residual neural network is defined as a linear least-square problem using the integral equation at the collocation points in the training set. The training iteration is done for the same set of parameters for different training sets. The numerical experiments show that the deep learning method is efficient with a moderate generalization error at all points. And the computational cost does not suffer from “curse of dimensionality” problem.

Algebraic-integer valued polynomials

For an integral domain R with field of fractions K≠R, absolute integral closure R‾ and a set W⊆R‾ let IntK(W,R‾) denote the ring of polynomials f∈K[X] that are R‾-valued on W. Let int(n,R) (resp. int(≤n,R)) denote the set of degree n (resp. degree ≤n) elements of R‾. In this article we focus on Global fields K and Dedekind domains R; without additional restrictions on R, we show that IntK(int(≤n,R),R‾)=IntK(int(n,R),R‾), for a given b∈R, we provide a characterization of the set of f∈R[X] with b−1f∈IntK(int(n,R),R‾) and a more precise identification if b is semi-reduced. We propose a natural generalization of the notion of a special sequence.

Comaximal factorization lattices

We extend some results of Brewer and Heinzer about integral domains with certain comaximal factorization properties for ideals, to the more general setup of multiplicative lattices.

Impact and contact problems of explosives by ‘Mixed’ meshless local Petrov-Galerkin finite volume method

The ‘Mixed’ Meshless Local Petrov-Galerkin Finite Volume method (MLPG5) is developed for solving low-velocity impact problems of plastic bonded explosives (PBX). Due to the ductility and plasticity of PBX, there is large deformation instead of pulverization or fragmentation. In this paper, the impact dynamics equations are solved by the meshless approach (MLPG5), both stress as well as displacements are interpolated, through the moving least squares (MLS) interpolation schemes, which eliminates the expensive process of domain integrals and differentiating the shape function. The collocation method is applied to enforce strain-displacement relationships only at each nodal point, instead of the subdomain. In the present mixed method, the independent interpolation of stress improves accuracies of both the plastic stress and contact stress. The contact force is obtained by penalty function method via iteration scheme. Due to the non-linear constitutive relation, the incremental stress is obtained via radial return schemes through Newton Raphson iteration. Finally, several numerical examples are given to demonstrate the feasibility and the accuracy of the present numerical approach compared with the finite element method. Numerical examples also demonstrate the advantages of the present methods: (i) smaller support sizes can be used; (ii) higher accuracies of stress are obtained.

Cancer’s camouflage: Microvesicle shedding from cholesterol-rich tumor plasma membranes might blindfold first-responder immunosurveillance strategies

Intermediary metabolism of tumors is characterized, in part, by a dysregulation of the cholesterol biosynthesis pathway at its rate-controlling enzyme providing the molecular basis for tumor membranes (mitochondria, plasma membrane) to become enriched with cholesterol (Bloch, 1965; Feo et al., 1975; Brown and Goldstein, 1980; Goldstein and Brown, 1990). Cholesterol enriched tumor mitochondria manifest preferential citrate export, thereby providing a continuous supply of substrate precursor for the tumor’s dysregulated cholesterogenesis via a “truncated” Krebs/TCA cycle (Kaplan et al., 1986; Coleman et al., 1997). Proliferating tumors shed elevated amounts of plasma membrane-derived extracellular vesicles (pmEV) compared with normal tissues (van Blitterswijk et al., 1979; Black, 1980). Coordination of these metabolic phenomena in tumors supports the enhanced intercalation of cholesterol within the plasma membrane lipid bilayer’s cytoplasmic face, the promotion of outward protrusions from the plasma membrane, and the evolution of cholesterol enriched pmEV. The pmEV shed by tumors possess elevated cholesterol and concentrated cell surface antigen clusters found on the tumor cells themselves (Kim et al., 2002). Upon exfoliation, saturation of the extracellular milieu with tumor-derived pmEV could allow early onset mammalian immune surveillance mechanisms to become “blind” to an evolving cancer and lose their ability to detect and initiate strategies to destroy the cancer. However, a molecular mechanism is lacking that would help explain how cholesterol enrichment of the pmEV inner lipid bilayer might allow the tumor cell to evade the host immune system. We offer a hypothesis, endorsed by published mathematical modeling of biomembrane structure as well as by decades of in vivo data with diverse cancers, that a cholesterol enriched inner bilayer leaflet, coupled with a logarithmic expansion in surface area of shed tumor pmEV load relative to its derivative cancer cell, conspire to force exposure of otherwise unfamiliar membrane integral protein domains as antigenic epitopes to the host’s circulating immune surveillance system, allowing the tumor cells to evade destruction. We provide elementary numerical estimations comparing the amount of pmEV shed from tumor versus normal cells.

New recognition specificity in a plant immune receptor by molecular engineering of its integrated domain

Plant nucleotide-binding and leucine-rich repeat domain proteins (NLRs) are immune sensors that recognize pathogen effectors. Here, we show that molecular engineering of the integrated decoy domain (ID) of an NLR can extend its recognition spectrum to a new effector. We relied for this on detailed knowledge on the recognition of the Magnaporthe oryzae effectors AVR-PikD, AVR-Pia, and AVR1-CO39 by, respectively, the rice NLRs Pikp-1 and RGA5. Both receptors detect their effectors through physical binding to their HMA (Heavy Metal-Associated) IDs. By introducing into RGA5_HMA the AVR-PikD binding residues of Pikp-1_HMA, we create a high-affinity binding surface for this effector. RGA5 variants carrying this engineered binding surface perceive the new ligand, AVR-PikD, and still recognize AVR-Pia and AVR1-CO39 in the model plant N. benthamiana. However, they do not confer extended disease resistance specificity against M. oryzae in transgenic rice plants. Altogether, our study provides a proof of concept for the design of new effector recognition specificities in NLRs through molecular engineering of IDs.

Role of Digital Skills in Refugee Integration

Two concurrent 21st-century phenomena—the nearly unprecedented number of forced migrants and the near ubiquity of information and communications technology—have given rise to increased scholarship in “digital migration studies.” One area of investigation in this emergent interdisciplinary field is the role of digital skills in refugee integration. Given the accelerated global reliance on technology resulting from the COVID-19 pandemic, the author conducted a state-of-the-art literature review to identify emerging issues and highlight research needs in this area. A search of 10 databases yielded 39 studies spanning the major resettlement regions (North America, Western Europe, Oceania), and including refugees from across the globe. The inclusion criteria were studies focused on refugees’ practical use of digital technology in integration, published from January 2020-April 2021. Exclusion criteria were studies on refugees in transit or protracted displacement, digital connectivity and accessibility, use of digital technology by humanitarian actors, software development, analyses of digital representations of refugees, public attitudes toward refugees as expressed in digital media, and literature reviews. Ndofor-Tah et al.’s (2019) Refugee Integration Framework was used to organize and synthesize the findings. The studies demonstrated how digital skills affect all domains of integration. Additionally, the studies confirm that many refugees in resettlement have limited digital skills for necessary integration tasks, such as navigating websites and assessing the credibility of online information. Limitations of this state-of-the-art review include its cross-sectional nature, having only one reviewer, and only published literature accessible online through public websites or subscription databases. An important emerging issue for future research is assessing, teaching, and learning digital skills among this population. The study's contributions to the knowledge base and theory, and its implications for information science scholars and practitioners and those in allied disciplines within digital migration studies, are discussed.

Enforcing essential boundary conditions on domains defined by point clouds

This paper develops and investigates a new method for the application of Dirichlet boundary conditions for computational models defined by point clouds. Point cloud models often stem from laser or structured-light scanners which are used to scan existing mechanical structures for which CAD models either do not exist or from which the artifact under investigation deviates in shape or topology. Instead of reconstructing a CAD model from point clouds via surface reconstruction and a subsequent boundary conforming mesh generation, a direct analysis without pre-processing is possible using embedded domain finite element methods. These methods use non-boundary conforming meshes which calls for a weak enforcement of Dirichlet boundary conditions. For point cloud based models, Dirichlet boundary conditions are usually imposed using a diffuse interface approach. This leads to a significant computational overhead due to the necessary computation of domain integrals. Additionally, undesired side effects on the gradients of the solution arise which can only be controlled to some extent. This paper develops a new sharp interface approach for point cloud based models which avoids both issues. The computation of domain integrals is circumvented by an implicit approximation of corresponding Voronoi diagrams of higher order and the resulting sharp approximation avoids the side effects of diffuse approaches. Benchmark examples from the graphics as well as the computational mechanics community are used to verify the algorithm. All algorithms are implemented in the FCMLab framework and provided at https://gitlab.lrz.de/cie_sam_public/fcmlab/. Further, we discuss challenges and limitations of point cloud based analysis w.r.t. application of Dirichlet boundary conditions.

Are Work Demand, Support and Control Associated with Work Ability and Disability during Back Pain Treatment? A Prospective Explorative Study

Background: Low back pain is a multifactorial disease with consequences for work ability and social participation. Improved integration of the work domain in health care management is needed. The aim of this study was to explore the relation between working conditions with outcome of low back pain treatment. Methods: Observational study of 41 patients attending physiotherapy for low back pain. Work demands, support and control were registered at baseline and work ability and disability also at baseline, with follow up after three and nine months. We used mixed-effects models to estimate the longitudinal associations between working conditions and outcome. Results: Higher work demands were related to reduced work ability (−1.1 points, 95% CI: −2.1 to −0.1) and slightly increased disability (5.6 points, 95% CI: 0.5 to 10.7). Lack of social support from colleagues was associated with reduced work ability (−2.7 points, 95% CI: −0.2 to 1.5) and disability (14.0 points, 95% CI: 4.9 to 23.1). Conclusions: This explorative study found associations between work demands and support, and work ability and disability outcome. Screening for psychosocial working conditions may influence the work ability and disability treatment outcome. The results need replication in larger samples and may indicate that patients seeking primary care management for low back pain should be screened for work demands, support and control.

Thermodynamic Properties of Liquid Toluene and n-Butane Determined from Speed of Sound Data

The method of thermodynamic integration is applied to calculate accurate data for the density and isobaric and isochoric heat capacity of toluene and n-butane from speed of sound data sets measured previously in our laboratory. Values for the density and isobaric heat capacity on the initial isobar for the integration are derived from very accurate density and speed of sound data sets using well-known thermodynamic relations. The relative expanded uncertainties (at the 0.95 confidence level) in the derived values for the density and isobaric and isochoric heat capacities are estimated to be 0.011 %, 0.3 %, and 0.4 % for toluene and 0.02 %, 0.5 %, and 0.7 % for n-butane, respectively. Comparisons with experimental data, values of other authors derived by the thermodynamic integration, and equations of state show that our values for both fluids are more accurate than most data available in the literature. Moreover, the domain of the thermodynamic integration for toluene extends down to 240 K and covers lower temperatures than recently considered by other authors. The derived values for the isobaric heat capacity of n-butane fill a gap as this property has hitherto only been measured at ambient pressure. Because of their low uncertainty, the values of the derived properties reported in this work in combination with recent data of other authors are useful for developing new and improved equations of state for both fluids.

The zinc-binding motif in tankyrases is required for the structural integrity of the catalytic ADP-ribosyltransferase domain.

Tankyrases are ADP-ribosylating enzymes that regulate many physiological processes in the cell and are considered promising drug targets for cancer and fibrotic diseases. The catalytic ADP-ribosyltransferase domain of tankyrases contains a unique zinc-binding motif of unknown function. Recently, this motif was suggested to be involved in the catalytic activity of tankyrases. In this work, we set out to study the effect of the zinc-binding motif on the activity, stability and structure of human tankyrases. We generated mutants of human tankyrase (TNKS) 1 and TNKS2, abolishing the zinc-binding capabilities, and characterized the proteins biochemically and biophysically in vitro. We further generated a crystal structure of TNKS2, in which the zinc ion was oxidatively removed. Our work shows that the zinc-binding motif in tankyrases is a crucial structural element which is particularly important for the structural integrity of the acceptor site. While mutation of the motif rendered TNKS1 inactive, probably due to introduction of major structural defects, the TNKS2 mutant remained active and displayed an altered activity profile compared to the wild-type.

Dual tunable angle filters on graphene and liquid crystal metamatial

In this paper, we realized a large angle filter in a composite structure with the metamaterial , which consists of graphene strips (GS), polyimide and liquid crystal (LC). We analyzed the transmission spectra to realize tunable filter by the finite integral time domain (FITD) method. The resonance frequencies had little change on low range and obvious red shift on high range which increasing the incident angle. The pass-band filter can be obtained at the angle reaches to 80°, so the large angle filter can be achieved in the structure. The filtering spectrum can be tuned by changing the voltage applied to the graphene layer and the LC layer respectively. The results are shown that the dual tunable multi-band filter can be realize in the designed structure. These results have many potential applications on filtering, large-angle switching and sensors. • A large angle filter in a composite structure with the metamaterial of the graphene and the liquid crystal layer is studied. • The dual tunable multi-band filter can be realize in the designed structure. • The filtering spectrum can be tuned by changing the voltage applied to the graphene layer and the LC layer respectively.

A Unified Solution Method for Free Vibration of Arbitrarily Shaped Plates without or with Cracks

This paper presents a new approach for analyzing the free vibration of thin plates with arbitrary piecewise smooth curvilinear contour under various boundary conditions. It can also be applied to plates with cracks. This approach is based on the transformation of energy integral expressions and the domain decomposition technique. Furthermore, boundary conditions are modeled by using linear springs to restrain the plate edges. For obtaining the expressions of energy integral, the arbitrarily shaped domain of integration is divided into several trapezoid domains with curved sides by a set of parallel lines passing through the intersection points of contour curve segments. Then, Jacobi orthogonal polynomials are introduced as the admissible functions, so that the repeated integrals in the energy expressions are reduced to definite integrals analytically. At this point, the calculation method of the energy functional is determined by the equation forms of the curve segments of the plate contour. When the equations of the curve segments allow the integrands to have analytic primitive functions, the energy functional has an analytical solution. Otherwise, the Gauss–Legendre method is used to obtain the numerical solution. Accordingly, the arbitrarily shaped plate with cracks is decomposed into several arbitrarily shaped subdomains based on the cracks. Each subdomain is handled according to the above procedure. The continuity conditions at the interconnecting interfaces of the subdomains are realized by linear springs. The plate without or with crack is modeled by setting the spring stiffness to infinity or 0. The accuracy of the proposed method is verified by comparing the obtained results with the published results. Furthermore, the vibration characteristics of plates with various shapes, such as astroid-shaped plates and cracked elliptical plates, are investigated. These new results can serve as benchmarks for further studies on the vibration of plates.

A comprehensive investigation of the formulations of the interaction integral method for the evaluation of stress intensity factors of three-dimensional cracks in functionally graded materials

The interaction integral for functionally graded materials can be expressed in a number of formulations. In this paper, some of the formulations that were found in the literature in addition to some new formulations are discussed. The discussion will focus on the postulates of elastic constants in deriving the interaction integral formulations in the form of domain integrals. Mode I and mixed-mode crack problems of functionally graded materials are presented. Then, the accuracies of the stress intensity factors computed by the presented interaction integrals are critically compared. It was found that all the SIFs computed by the presented formulations are equally accurate.

Computational co-design framework for coreless wound fibre–polymer composite structures

AbstractIn coreless filament winding, resin-impregnated fibre filaments are wound around anchor points without an additional mould. The final geometry of the produced part results from the interaction of fibres in space and is initially undetermined. Therefore, the success of large-scale coreless wound fibre composite structures for architectural applications relies on the reciprocal collaboration of simulation, fabrication, quality evaluation, and data integration domains. The correlation of data from those domains enables the optimization of the design towards ideal performance and material efficiency. This paper elaborates on a computational co-design framework to enable new modes of collaboration for coreless wound fibre–polymer composite structures. It introduces the use of a shared object model acting as a central data repository that facilitates interdisciplinary data exchange and the investigation of correlations between domains. The application of the developed computational co-design framework is demonstrated in a case study in which the data are successfully mapped, linked, and analysed across the different fields of expertise. The results showcase the framework’s potential to gain a deeper understanding of large-scale coreless wound filament structures and their fabrication and geometrical implications for design optimization.

A Mixed Finite Differences Scheme for Gradient Approximation

In this paper, we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective function is costly or the objective function values are affected by some noise. These functionals have been recently considered to estimate the gradient of the objective function by the expected value of the function variations in the space of directions. The expected value is then approximated by a sample average over a proper (random) choice of sample directions in the domain of integration. In this way, the approximation error is characterized by statistical properties of the sample average estimate, typically its variance. Therefore, while useful and attractive bounds for the error variance can be expressed in terms of the number of function evaluations, nothing can be said on the error of a single experiment that could be quite large. This work instead is aimed at deriving an approximation scheme for linear functionals approximating the gradient, whose error of approximation can be characterized by a deterministic point of view in the case of noise-free data. The previously mentioned linear functionals are no longer considered as expected values over the space of directions, but rather as the filtered derivative of the objective function by a Gaussian kernel. By using this new approach, a gradient estimation based on a suitable linear combination of central finite differences at different step sizes is proposed and deterministic bounds that do not depend on the particular sample of points considered are computed. In the noisy setting, on the other end, the variance of the estimation error of the proposed method is showed to be strictly lower than the one of the estimation error of the Central Finite Difference scheme. Numerical experiments on a set of test functions are encouraging, showing good performances compared to those of some methods commonly used in the literature, also in the noisy setting.