Local Basis Research Articles

Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters

This article presents a novel method to accurately simulate electromagnetic scattering at homogeneous polygonal cylinders with arbitrary material properties. A single source equivalence approach is invoked, allowing to substitute the background medium for the inner material of the scatterer, provided an equivalent surface current density is introduced. We construct the pertinent differential surface admittance operator by means of the Fokas method, establishing a map between the known Dirichlet boundary values and their unknown Neumann counterparts. However, to allow for lossy materials, we extend the Fokas method to complex wavenumbers. The novel formalism, employing pulse-shaped local basis functions, natively supports combined magnetic and dielectric contrast, accurately captures the skin effect, and is conveniently integrated in traditional boundary integral equation formulations. The correctness and versatility of our technique are verified for various examples by means of analytical validation and through comparison with a Poggio-Miller-Chan-Harrington-Wu-Tsai approach, a volume integral equation method and a commercial solver.

A Reduction Technique for the Calculation of the Forced Response of Bladed Disks in the Presence of Contact Mistuning at Blade Root Joints

Abstract The effect of differences in nominally equal sectors of a bladed disk (mistuning) is a well-known problem for designers since the forced response may show localized amplification of the blade response with respect to a cyclically symmetric (tuned) configuration. In order to perform a large number of simulations in a reasonable amount of time to characterize the highest blade response, corresponding to the worst mistuning pattern, reduction techniques have been developed, where the mistuning is introduced directly in a compact, reduced order model (ROM) obtained from very large finite element (FE) models. Typically, mistuning is introduced in the ROM in terms of natural frequency perturbations of the blade; nevertheless, a better insight is specifically required in order to correlate mistuning to a specific source (geometrical, material, contact mistuning). In this paper, a reduction technique is presented to take into account mistuning due to the contact uncertainties at the blade root joint, which can be caused by design tolerances, manufacturing process, assembly procedures, wear, etc. The technique takes its basis from the Craig–Bampton component mode synthesis (CB-CMS) applied to the uncoupled blade and disk sector, which is typically included in most of the FE software for easy implementation in standard industrial practice. The full set of master degrees-of-freedom (DOFs) at the random contacts are purposely reduced using an optimal local modal basis based on the Gram–Schmidt interface (GSI) technique developed by the authors. Experimental evidence of actual uncertain contact obtained during joint preloading is used to find an appropriate base to represent typical contact patterns.

How to improve issuing, transfusion and follow-up of blood components in Southern and Eastern Mediterranean countries? A benchmark assessment

To determine the existence of guidelines regarding the appropriate clinical use of blood and blood components, transfusion requests, and blood issuing/reception documents and procedures. The different bedside transfusion organizations/processes and hemovigilance are also analyzed. The ultimate objective is to identify safe potential options in order to improve blood safety at the lowest cost. Data emanating from eight Arabic eastern/southern Mediterranean countries who responded to five surveys were collected and tabulated. National recommendations for the clinical use of blood components especially for hemoglobinopathies are lacking in some countries. In matter of good practices in the prescription, issuing and reception of BCs, efforts were made either on national or local basis. Procedures regarding patient information and ethical issues are still lacking. Almost all Mediterranean countries apply two blood testing procedures on each patient sample. Only Morocco, Tunisia and Algeria perform bed side blood group testing; Egypt and Lebanon perform antibody screen and antiglobulin cross matching universally. Automation for blood testing is insufficiently implemented in almost all countries and electronic release is almost absent. National hemovigilance policy is implemented in Tunisia, Morocco, and Lebanon but the reporting system remains inoperative. Insufficient resources severely hinders the implementation of expensive procedures and programs; however, the present work identifies safe procedures that might save resources to improve other parts in the transfusion process (e.g. electronic release to improve safety in issuing). Moreover, setting up regulations regarding ethics in transfusing recipients along with local transfusion committees are crucially needed to implement hemovigilance in transfusion practice.

Super-localization of elliptic multiscale problems

Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a d d -dimensional domain. The application of the inverse operator to some standard finite element space defines an approximation space with uniform algebraic approximation rates with respect to the mesh size parameter H H . This holds even for under-resolved rough coefficients. However, the true challenge of numerical homogenization is the localized computation of a localized basis for such an operator-dependent approximation space. This paper presents a novel localization technique that leads to a super-exponential decay of its basis relative to H H . This suggests that basis functions with supports of width O ( H | log ⁡ H | ( d − 1 ) / d ) \mathcal O(H|\log H|^{(d-1)/d}) are sufficient to preserve the optimal algebraic rates of convergence in H H without pre-asymptotic effects. A sequence of numerical experiments illustrates the significance of the new localization technique when compared to the so far best localization to supports of width O ( H | log ⁡ H | ) \mathcal O(H|\log H|) .

GEOGRAPHICAL STUDIES OF TOPONYM OF KHMELNYTSKYI REGION

The study and research of geographical names, a separate administrative region, makes it possible to analyze how the influence and role of natural resources, the history of settlement and development of the territory have affected the life of the population. Geographical nomenclature of a certain territory is called toponymy of this region. Toponymy is especially important for such disciplines as physical geography, topography, local history, historical geography, cartography, economic and social geography.
 In this article the concept of toponyms is considered, their classification is given. The toponymic zoning of Khmelnytskyi region is proposed. The influence of geographical, historical, cultural conditions on the emergence of toponyms of Khmelnytskyi region is investigated. The process of decommunization and derussification of geographical names of the studied territory is highlighted.
 The analysis of the source base shows that the toponymy of Khmelnytskyi region is closely connected with the history of the region, especially with its settlement. The toponymic system of Khmelnytskyi region under the influence of different epochs underwent constant changes that influenced the process of toponym formation.
 After analyzing the formation of the names of 131 rivers in Khmelnytskyi region, the length of which is more than 10 km, we obtained the following results: the largest number of names are formed by the characteristic properties (features) of water bodies, namely 23.3%. Also, a large number of names are related to the location of the water body - 20%. The smallest number of names are related to soil features - 1.5%. Of the 18 analyzed names of lakes in Khmelnytskyi region, the largest number of names are associated with the location of the water body, namely 6 names (Lake Krugle, Lake Ezerske, Lake Novostavske, Lake Terebizh, Lake Lisova Pisnya, Lake Lisove).
 Comonyms and astionyms of Khmelnytskyi region are divided into thirteen groups. The largest number of names of rural settlements are derived from a person's own name or surname (37.3%). Out of 37 analyzed astionyms 16 belong to anthroponyms. The largest number of settlements whose names are derived from a person's own name or surname. The smallest number oikonyms are of memorial origin (1.5%)
 On the basis of spatial localization of types of settlements similar in topoformant and uniqueness of their correlation, objectively existing hierarchical units of zoning were distinguished. The calculation of morphometric, as well as spatial toponymic characteristics of oikonyms of Khmelnytsky region, allowed to allocate: Volyn macro-region (1 rayon and 2 sub-rayons); Podil macro-region (3 rayons and 9 sub-rayons); Pivdenopodilskyi macro-region (2 rayons and 4 sub-rayons).
 Within the framework of decommunization and de-Russification in the Khmelnytskyi region during 2022, more than 800 streets and lanes were renamed, and about 1300 more objects should be renamed.
 Prospects for using the results of the study. The materials of this publication can be used for further decommunization and de-Russification of geographical names in Khmelnytskyi region. The developed scheme of toponymic zoning of Khmelnytskyi region can be taken into account in the toponymic zoning of the territory of Ukraine.
 Key words: toponyms, homonyms, hydronyms, oikonyms, decommunization, de-Russification.

The Influence of Converting Food Crops to Forage Crops Policy Implementation on Herbivorous Livestock Husbandry Development—Based on Policy Pilot Counties in Hebei, China

In the context of increasing consumption of herbivorous livestock products, competition between humans and animals for food, and increasing environmental constraints, it is necessary to solve the problem of sustainable development of China’s livestock industry and increase the protection and development of the grassland livestock industry while making good use of production resources in agricultural areas in order to explore the development potential of the herbivorous livestock industry in agricultural areas. The Converting Food Crops to Forage Crops Policy (CFFP), as an important measure of agricultural supply-side structural reform, aims to develop a high-quality forage industry and a high-quality herbivorous livestock industry. However, over the years of policy implementation, few studies have examined the impact effects of the policy on the development of the regional herbivorous livestock industry. To fill this research gap and provide theoretical support for subsequent policy implementation, the study used the synthetic control method to examine the impact of policy implementation on the development of herbivorous livestock production in the pilot counties in Hebei Province from 2010 to 2020. The study discovered that the policy’s implementation encouraged the expansion of herbivorous livestock production in the pilot counties, but the policy’s effects on various regions and livestock species varied due to the influence of local production bases and resource endowments.

Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics

This paper formulates the second-order BDF and theta schemes based on an efficient localized meshless technique for computing the approximate solution of the Sobolev model. The model is one of the useful description for modeling the flow of fluids through fractured rocks, movement of moisture in soils. This proposed approach discretizes the nonlinear Sobolev equation in two main steps. In the first step, temporal discretization is accomplished with the help of the second-order BDF and theta schemes, respectively. In the second step, the localized radial basis function partition of unity collocation method (L-RBF-PUCM) is used for spatial discretization, thereby constructing a fully-discrete algorithm. For large linear problems, global techniques have the disadvantage of high computational cost. The proposed method overcomes this shortcoming well and reduces the computational burden by sparsifying the linear system. The convergence analysis and unconditional stability of the semi-discrete formulation are examined by means of the energy method. Numerical results are carried out to verify the validity and accuracy of the L-RBF-PUCM.

4-dimensional local radial basis function interpolation of large, uniformly spaced datasets

Background and ObjectiveLarge, uniformly spaced, complex and time varying datasets derived from high resolution medical image velocimetry can provide a wealth of information regarding small-scale transient physiological flow phenomena and pulsation of anatomical boundaries. However, there remains a need for interpolation techniques to effectively reconstruct a fully 4-dimensional functional relationship from this data. This paper presents a preliminary evaluation of a 4-dimensional local radial basis function (RBF) algorithm as a means of addressing this problem for laminar flows. MethodsA 4D interpolation algorithm is proposed based on a Local Hermitian Interpolation (LHI) using a combination of multi-quadric RBF with a partition of unity scheme. The domain is divided into uniform sub-systems with size restricted to immediately neighbouring points. The validity of the algorithm is first established on a known 4D analytical dataset and a CFD based laminar flow phantom. Application is then demonstrated through characterisation of a large 4D laminar flow dataset obtained from magnetic resonance imaging (MRI) measurements of cerebrospinal fluid velocities in the brain. ResultsPerformance of the algorithm is compared to that of a quad-linear interpolation, demonstrating favourable improvement in accuracy. The technique is shown to be robust, computationally efficient and capable of refined interpolation in Euclidean space and time. Application to MR velocimetry data is shown to produce promising results for the 4D reconstruction of the transient flow field and movement of the fluid boundaries at spatial and temporal locations intermediate to the original data. ConclusionThis study has demonstrated feasibility of an accurate, stable and efficient 4-dimensional local RBF interpolation method for large, transient laminar flow velocimetry datasets. The proposed approach does not suffer from ill-conditioning or high computational cost due to domain decomposition into local stencils where the RBF is only ever applied to a limited number of points. This work offers a potential tool to assist medical diagnoses and drug delivery through better understanding of physiological flow fields such as cerebrospinal fluid. Further work will evaluate the technique on a wider range of flow fields and against CFD simulation.

Equally spaced points are optimal for Brownian Bridge kernel interpolation

In this paper we show how ideas from spline theory can be used to construct a local basis for the space of translates of a general iterated Brownian Bridge kernel kβ,ɛ for β∈N, ɛ≥0. In the simple case β=1, we derive an explicit formula for the corresponding Lagrange basis, which allows us to solve interpolation problems without inverting any linear system.We use this basis to prove that interpolation with k1,ɛ is uniformly stable, i.e., the Lebesgue constant is bounded independently of the number and location of the interpolation points, and that equally spaced points are the unique minimizers of the associated power function, and are thus error optimal. In this derivation, we investigate the role of the shape parameter ɛ>0, and discuss its effect on these error and stability bounds.Some of the ideas discussed in this paper could be extended to more general Green kernels.

A Fitting Recognition Approach Combining Depth-Attention YOLOv5 and Prior Synthetic Dataset

To address power transmission lines (PTLs) traveling through complex environments leading to misdetections and omissions in fitting recognition using cameras, we propose a fitting recognition approach combining depth-attention YOLOv5 and prior synthetic dataset to improve the validity of fitting recognition. First, datasets with inspection features are automatically synthesized based on prior series data, achieving better results with a smaller data volume for the deep learning model and reducing the cost of obtaining fitting datasets. Next, a unique data collection mode is proposed using a developed flying-walking power transmission line inspection robot (FPTLIR) as the acquisition platform. The obtained image data in this collection mode has obvious time-space, stability, and depth difference, fusing the two data types in the deep learning model to improve the accuracy. Finally, a depth-attention mechanism is proposed to change the attention on the images with depth information, reducing the probability of model misdetection and omission. Test field experiments results show that compared with YOLOv5, the mAP5095 (mean average precision on step size 0.05 for thresholds from 0.5 to 0.95) of our depth-attention YOLOv5 model for fitting is 68.1%, the recall is 98.3%, and the precision is 98.3%. Among them, AP, recall, and precision increased by 5.2%, 4.8%, and 4.1%, respectively. Test field experiments verify the feasibility of the depth-attention YOLOv5. Line field experiments results show that the mAP5095 of our depth-attention YOLOv5 model for fittings is 64.6%, and the mAPs of each class are improved compared with other attention mechanisms. The inference speed of depth-attention YOLOv5 is 3 ms slower than the standard YOLOv5 model and 10 ms to 15 ms faster than other attention mechanisms, verifying the validity of the depth-attention YOLOv5. The proposed approach improves the accuracy of the fitting recognition on PTLs, providing a recognition and localization basis for the automation and intelligence of inspection robots.

An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows

This paper focusses on the numerical technique based on a localized meshless collocation method for approximating the Burgers-type equation in two dimensions. The method uses two main stages to approximate the unknown solution. First, the time derivative is discretized by the backward Euler method and a semi-discrete approach is obtained. Meanwhile, the unconditional stability and convergence of the semi-discrete scheme are proved by virtue of the discrete energy method in an appropriate Sobolev space. Second, a local radial basis function partition of unity (LRBF-PU) method is applied to approximate the spatial direction and a fully-discrete scheme is established. The LRBF-PU is based on subdividing the original domain to several subdomains and uses the radial basis function interpolation on each local subdomain. Compared with the global collocation technique, the main advantages of this technique are that it can reduce the computational cost and obtain a well linear system. Three illustrative examples are presented to demonstrate the accuracy and efficiency of the proposed method.

Prevalence and Effect of Stroke Associated Pneumonia on in-Hospital Stay, Mortality and Functional Outcome at Discharge from Hospital

Background and Aim: Stroke is the most prominent cause of morbidity and mortality worldwide especially in developing countries. The stroke outcome mainly related to the presence of complications and severity. Stroke associated pneumonia is the post stroke infection significantly associated with a longer hospitalization, increased risk of hospital mortality, and functional outcomes. There is scarcity of data regarding stroke associated pneumonia on a local basis in the developing countries. Therefore, present study aimed to find out the prevalence and effect of stroke associated pneumonia on in-hospital stay, mortality, and function outcome. Methodology: This observational prospective study was conducted on 500 stroke patients in the Department of Neurology and Medicine, Jinnah Hospital, Lahore from April 2021 to March 2022. Prior to study conduction, written informed consent and ethical approval was taken. All the participants were recruited for this study. Stroke was diagnosed based on relevant clinical history, brain imaging either by CT scan or MRI, and focused physical examination. Stroke patients of either gender above 18 years age with acute ischemic or hemorrhagic stroke and given written consent were included. All those patients who are already having disability due to previous stroke and other neurological or non-neurological issues were excluded from study. Baseline characteristics were recorded. SPSS version 25 was used for data analysis. Results: Of the total 500 stroke patients, there were 232 (46.4%) male and 268 (53.6%) females. The overall mean age was 62.4 ± 12.6 years. The prevalence of ischemic and hemorrhagic stroke was 334 (66.8%) and 166 (33.2%) respectively among 500 stroke patients. Hemiparesis was the most prevalent neurological findings 464 (92.8%) followed by facial palsy 432 (86.4%) and swallowing disturbance 262 (52.4%). About 186 (37.2%) stroke patients were complicated by stroke associated pneumonia. Multivariate regression analysis was used and revealed that stroke associated pneumonia could be developed in older age patients > 70 years Adjusted odd ratio AOR= 3.862 (1.21-12.86) (p=0.031) who suffered from swallowing disturbance AOR= 4.728, (2.415-9.102) (p<0.001), epileptic seizures AOR= 2.749 (1.315-5.681) (p<0.001), and moderate to severe stroke AOR= 6.183 (2.036-17.647) (p<0.001) (NIHSS=16-21). Conclusion: The present study concluded that prevalence of SAP was 37.2%. Stroke associated pneumonia is a significant medical issue or complications in stroke patients. Furthermore, older stroke patients with epileptic seizure, swallowing disturbance, and stroke severity from moderate to severe were the risk factors for increasing stroke associated pneumonia. Close monitoring and effective intervention might be needed for high risk SAP in stroke patients. Keywords: Stroke associated pneumonia, Functional outcome, Mortality, Hospital stay, Stroke

Neighborhood rough set based ensemble feature selection with cross-class sample granulation

Exploring feature significance associated with label is a fundamental task in the architecture of feature selection. Nevertheless, most of the existing schemes are limited by the global feature significance over the entire universe. It follows that some specific characteristics of features implied in sample subspaces may be overlapped. To fill such a gap, a novel ensemble feature selection with cross-class sample granulation is developed. Our method explicitly involves two main phases: (1) cross-class sample granulation — data is separated into multiple granules which are generated by querying the locations of samples in their respective classes, so as to provide local bases; (2) ensemble feature selection — localized evaluations of feature significance are integrated which are induced by leveraging multiple homogeneous fine-granularity measures from those bases, so as to select qualified features. To validate the effectiveness of our proposed method, it is compared with several well-established feature selection schemes in CART, KNN and SVM classification performance. Experimental results on 20 UCI data sets demonstrate that our method is superior as it yields higher accuracy with satisfactory elapsed time.

Addressing Capacity Constraints of Rural Local Health Departments to Support Climate Change Adaptation: Action Is Needed Now.

Looming climate change health impacts among rural communities will require a robust health system response. To reduce health inequities and promote climate justice, rural local health departments (LHDs) must be adequately resourced and supported to engage in climate change mitigation and adaptation policy and program development and implementation. In the United States, small local tax bases, overreliance on revenue from fee-based services, and limited federal funding to support climate change and health programming, have left rural LHDs with limited and inflexible human, financial, and political capital to support engagement in local climate change activities. Because of the urgent demands stemming from climate change, additional investments and supports are needed to rapidly build the capacity and capability of rural LHDs. Federal and state approaches to public health funding should consider the unique climate change and health risks of rural communities. Further, cross-jurisdictional shared service arrangements and state-level support to build rural LHDs’ technical capacity, and research on local impacts and culturally appropriate solutions, must be prioritized.

Conjugate MHD natural convection of hybrid nanofluids in a square enclosure containing a complex conductive cylinder

PurposeThe purpose of this study is to investigate the enhancement and suppression of heat transfer for hybrid nanofluids (Cu–Al2O3/water) in a square enclosure containing a thermal-conductive cylinder when the Lorentz force is applied to the hybrid nanofluids.Design/methodology/approachSince the inner conductive cylinder in present research has a complex geometry, an in-house meshless method, namely, the local radial basis function (LRBF) method, is applied to solve the 2 dimensional (2D) incompressible Navier–Stokes equation in the fluid domain and Fourier heat conduction equation in solid domain. The solid–fluid interface remains the physical continuity of temperature and heat flux. Only the Lorentz force is considered for the presence of the magnetic field. The conjugate natural convection is assumed to be steady, thus only fully developed heat exchange from the nanofluids to solid or vice versa is comprehensively investigated.FindingsIt can be concluded that Lorentz force plays a more significant role than hybrid nanofluids in enhancing/suppressing heat transfer when the orientation of magnetic field is the same to the x direction. The thermal conductivity ratio can dramatically change the isotherms and streamlines as well as the mean value of the Nusselt number, resulting in totally different heat transfer phenomena. The included angle of magnetic field also has a significant effect on the heat transfer rate when it changes from horizontal to vertical.Research limitations/implicationsThe constant thermo-physical properties of incompressible fluid and the 2D steady flow are considered in this study.Originality/valueThe conjugate MHD natural convection of hybrid nanofluids is numerically investigated by an in-house meshless LRBF method. The enhancement and suppression of heat transfer under the combined influence of the volume fraction of nanoparticles, Hartmann number and the thermal conductivity ratio are comprehensively investigated.

Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons

A comprehensive picture of polaron and bipolaron physics is essential to understand the optical absorption spectrum in many materials with electron-phonon interactions. In particular, the finite-temperature properties are of interest since they play an important role in many experiments. Here, we combine the parallel two-site time-dependent variational principle algorithm (p2TDVP) with local basis optimization (LBO) and purification to calculate time-dependent current-current correlation functions. From this information, we extract the optical conductivity for the Holstein polaron and bipolaron with dispersive phonons at finite temperatures. For the polaron in the weak and intermediate electron-phonon coupling regimes, we analyze the influence of phonon dispersion relations on the spectra. For strong electron-phonon coupling, the known result of an asymmetric Gaussian is reproduced for a flat phonon band. For a finite phonon bandwidth, the center of the Gaussian is either shifted to larger or smaller frequencies, depending on the sign of the phonon hopping. We illustrate that this can be well understood by considering the Born-Oppenheimer surfaces. A similar behavior is seen for the bipolaron for strong coupling. For the bipolaron with weak and intermediate coupling strengths and a flat phonon band, we obtain two very different spectra. The latter also has a temperature-dependent resonance at a frequency below the phonon frequency.

Interference of nuclear wavepackets in a pair of proton transfer reactions

Quantum mechanics revolutionized chemists' understanding of molecular structure. In contrast, the kinetics of molecular reactions in solution are well described by classical, statistical theories. To reveal how the dynamics of chemical systems transition from quantum to classical, we study femtosecond proton transfer in a symmetric molecule with two identical reactant sites that are spatially apart. With the reaction launched from a superposition of two local basis states, we hypothesize that the ensuing motions of the electrons and nuclei will proceed, conceptually, in lockstep as a superposition of probability amplitudes until decoherence collapses the system to a product. Using ultrafast spectroscopy, we observe that the initial superposition state affects the reaction kinetics by an interference mechanism. With the aid of a quantum dynamics model, we propose how the evolution of nuclear wavepackets manifests the unusual intersite quantum correlations during the reaction.

Angles between subspaces and nearly optimal approximation in GFEM

The Generalized Finite Element Methods (GFEM) are known for accurately resolving local features in heterogeneous media. Recent numerical experiments have shown that the use of local bases made from A-harmonic extensions of well chosen boundary data have nearly optimal approximation properties. In this paper we show that the explanation is geometric and given by the angle between any finite dimensional approximation space and the optimal finite dimensional approximation space introduced in (Babǔska and Lipton, 2011). The effect of the angle is quantified by an upper bound on the convergence rate. This rate is seen in the numerical simulations where local bases with nearly optimal approximation properties are identified.

Detecting nontrilocal correlations in a triangle network

Correlations in quantum networks with independent sources exhibit a completely novel form of nonclassicality in the sense that the nonlocality of such correlations can be demonstrated in fixed local input scenarios. Before the pioneering work by M.O.Renou, et al., in [1], the nonlocal feature of such network correlations was directly attributable to standard Bell nonlocality. In [1], the authors provided some of the first examples of triangle network correlations, whose nonlocality cannot be deduced from Bell-CHSH nonlocality. To date, a complete characterization of such scenarios is yet to be provided. Present work characterizes correlations arising due to fixed local measurements in a triangle network under a source independence assumptions. Precisely speaking, a set of criteria is framed in the form of Bell-type inequalities, each of which is necessarily satisfied by trilocal correlations. Possible quantum violation of at least one criterion from the set is analyzed, which in turn points out the utility of the set of criteria to detect nonlocality (nontrilocality) in quantum triangle networks. Interestingly, measurement on a local product state basis turns out to be sufficient to generate nontrilocal correlations in some quantum networks. Noise tolerance of the detection criteria is discussed followed by a generalization of the framework for demonstrating correlations in any n-sided polygon where n is finite.

Numerical simulation of 3D double-nozzles printing by considering a stabilized localized radial basis function collocation method

In this work, a stabilized local radial basis function collocation method (LRBFCM) is proposed to simulate the electrochemical 3D double-nozzles printing. A forward Euler-method is proposed to discretize time in the fluid flow described by Navier-Stokes (NS) equations. The background fictitious grids or meshes are employed to enhance the stability of the LRBFCM in solving the fluid flow. The details of the LRBFCM for simulating the pressure and velocity fields of the electrolyte during the electrochemical 3D printing process are introduced. The accuracy of the proposed method is validated by corresponding experiments, and good agreement can be observed between the numerical results and the experimental measurements.