Nodal Points Research Articles

Steady‐state operating points of islanded virtual synchronous machine microgrid

AbstractBefore starting stability analysis of the multivirtual synchronous machine (n‐VISMA) power system, it is necessary to obtain the steady‐state operating points (SSOPs) of all dynamic nodes in the network. Modified traditional iterative schemes using the concept of droop bus technique in an islanded microgrid are not feasible for load flow analysis of VISMA microgrid incorporating non‐control dynamics. This paper proposes closed‐form steady‐state, fundamental‐frequency models for islanded VISMA microgrids using the concept of virtual swing buses. In this technique, the virtual internal buses of all VISMAs in the network are governed by the swing equation. The voltage at all buses is variable except the virtual buses in which the pole wheel voltages are prespecified. The algorithm was extended by a droop control localized to each VISMA. The suitability of the proposed algorithm to obtaining SSOPs of VISMA was tested on IEEE‐9 bus system with VISMA replacing electromechanical synchronous machines and also on a low‐voltage distribution system. To validate the applicability of the proposed algorithm and prove its accuracy, the case study systems were also modeled in the SIMULINK environment for detailed time domain analysis. The algorithm was found to be computationally effective for a load flow analysis of the VISMA microgrid. The results also reveal that the addition of external droop control improves the frequency stability of the system.

Andreev bound states in Josephson junctions of semi-Dirac semimetals

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor–barrier–superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum ɛ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of ɛ on the superconducting phase difference ϕ, we compute the variation of Josephson current as a function of ϕ.

Investigating the Response Variability of Statically Determined Sandwich Beams considering two Random Fields of Elastic Modulus

In this paper, the displacement variation in sandwich beams is determined by employing a semi-analytical approach. The classical displacement is calculated by integration using Mohr’s equation, although the integration is complicated due to the inclusion of random fields in the inertial moment term. Using the trapezoidal rule to compute these integrals, the random fields are discretized into random variables at the nodal point of the beam segments. Thus, the expected displacement, standard deviation, and coefficient of variation can be computed. To validate the results, the random fields are simulated using a previously described spectral method. The results of numerical examples were compared with the semi-analytical method and the Monte Carlo simulation demonstrating the high accuracy of the proposed method. The results also illustrate the influence of the parameters of the random fields of elastic modulus on the variability of displacement.

Dynamics of 2 × 2 matrix non-Hermitian quantum systems on Bloch sphere

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely, the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point (EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

Accelerating high order discontinuous Galerkin solvers using neural networks: Wall bounded flows

High order solvers are accurate but computationally expensive as they require small time steps to advance the solution in time. In this work we include a corrective forcing to a low order solution to improve the accuracy while advancing in time with larger time steps, and achieve fast computations. The work uses a discontinuous Galerkin framework, where the polynomial order, inside each mesh element, can be varied to provide low or high accuracy. The corrective forcing is included for each high order Gauss nodal point in the mesh. This work is a continuation of [1, 2], where we extend the methodology to wall bounded flows. Namely, we adapt the methodology to a turbulent channel at Reτ = 182. In this case, we use three neural networks to correct different regions of the flow, which are distinguished by their y+ distance to the wall. The methodology is able to correct the low resolution simulation to attain flow statistics that are comparable to high order simulations. We include comparisons for the mean, Reynolds stresses and shear stress on the wall. We achieve good predictions using the corrected low order solution, in mean velocity and its corresponded fluctuations, as well as the shear stress on the wall.

Sinc approximation for solving fourth-order pseudo-Poisson equations

In this article, we will investigate the Galerkin sinc approximation to solve the single pseudo-Poisson problem and in this method we will reach a linear system. We will solve this system by carefully choosing the length of the steps and the number of nodal points and with two methods; the first method, which is the usual method, is theoretically flawed and not practical and computationally efficient. Therefore, to solve the mentioned system, we introduce the orthogonalization technique, which solves both theoretical and computational problems. Numerical approximation is obtained whose accuracy is exponential and of order where N is a transaction parameter and c is a constant independent of N. In the final part, we give some numerical examples of individual pseudo-Poisson problems to demonstrate the efficiency of the method.

Структура вихревых полей в волноводе пекериса с учетом дислокаций

Vortex fields are the most complex and least studied objects in the acoustics of layered media. They significantly complicate the structure of the sound field due to the appearance of nodal and saddle points in it, in the vicinity of which the concept of the phase of the sound wave becomes uncertain. Therefore, such special points of the sound field are usually called phase front dislocations. In turn, the dislocation structure of the vortex field is most complex in waveguides, which play an extremely important role in theoretical and applied hydroacoustics. In this work, the vortex structure of the sound field and the corresponding dislocation structure of the vortex field are analyzed using the example of a Pekeris waveguide, the sound field in which is constructed within the framework of a non-self-adjoint model formulation of the corresponding boundary value problem.

Optimal with Respect to Accuracy Recovery of Some Classes Functions by Fourier Series

Introduction. Function approximation (approximation or restoration) is widely used in data analysis, model building, and forecasting. The goal of function approximation is to find the function that best approximates the original function. This can be useful when the original function is too complex to analyze or when a model needs to be simplified for more efficient computation or interpretation. Function approximation is an important tool in science, engineering, economics, and other fields where data analysis and modeling are required. It allows you to simplify complex functions, identify patterns in the behavior of the object of study, and predict the value of a function beyond the available data. The purpose of the paper is consider the problems of approximation of a function, which on some interval is given by its values in some set of nodal points and belongs to some class of functions by trigonometric Fourier series with a given accuracy and at fulfillment of given constraints on its execution time. The main attention is paid to obtaining estimates of computational complexity (implementation time) and solving the problem of function approximation by Fourier series with a given or maximum possible accuracy using efficient algorithms for solving optimization problems. Results. The general formulation of the problem of approximation of functions by Fourier series in accordance with the technology of solving problems of computational and applied mathematics with specified values of quality characteristics is presented. Estimates of the error of the proposed approximation algorithms using for the computation of Fourier coefficients the optimal in accuracy and close to them quadrature formulas for the computation of integrals from rapidly oscillating functions of the classes of Helder and Lipschitz with given fixed values in the nodes of a fixed grid are given. The corresponding quadrature formulas and constructive estimates of the error of the method of approximation of functions of the specified classes are given. Estimates of computational complexity of the given algorithms are obtained, which allow us to set real constraints on the time of algorithm implementation with a given or maximum possible accuracy. Conclusions. A comprehensive analysis of the quality of the considered algorithms for the approximation of functions by Fourier series using the accuracy-optimal (or close to them) quadrature formulas for the computation of Fourier coefficients for the computation of integrals from rapidly oscillating functions is presented. The estimates of their main characteristics – accuracy and computational complexity – are obtained. Keywords: function approximation, Fourier series, Fourier series coefficients, approximation error, computational complexity.

ЭНЕРГЕТИЧЕСКИЕ СВОЙСТВА СИММЕТРИЧНЫХ ДЕФОРМИРУЕМЫХ СИСТЕМ

Energy methods for calculating structures, which have become popular for a century, are based on the Lagrange principle and have the meaning of equality of work of external forces and internal forces. Having proved their effectiveness in the overwhelming majority of problems of structural mechanics, they became the dominant approach in formulating the problems of studying solid deformable systems and gave rise to the main methodology for solving problems. As a result, a situation has arisen that the internal potential energy of a deformed body remains insufficiently studied.
 The paper develops an approach to the study of the symmetric structure at critical levels of strain energy. The criterion of critical levels of strain energy, based on the concepts of "self-stress" ("self-balance") of a deformable body. Limiting values of the structure strain energy may get by varying the reactions and deflections in the nodal points. The extreme values of forces and displacements of the rods are calculated in matrix form from the values of nodal reactions (displacements).
 Methodology for studying the energy properties of a system is shown on the examples of the study of symmetric rod systems without involving the concept of external forces. The technique is based on matrix methods of structural mechanics and the mathematical apparatus of eigenvalue problems. The comparison of structural design and structural analysis solution of structural mechanics tasks by traditional methods and with the proposed methodology is carried out.

Analysis and application of MLPG7 for diffusion equations with nonlinear reaction terms

This paper extends the recently proposed variant of meshless local Petrov Galerkin (MLPG) method, i.e., MLPG7, for solving time dependent PDEs. As test function, the method uses a novel modification of fundamental solution of Laplace operator that not only the test function itself but also its derivative vanish on boundary of local subdomains. Therefore, more stable local integral equations are obtained by replacing a boundary integral of derivatives of field variables with a domain integral of field variables itself. MLPG7 formulation converts the nonlinear governing equation into a system of first order ordinary differential equations (ODEs). For this system of ODEs, a theoretical stability analysis is carried out for the case of regularly spaced nodal points. Stability and convergence conditions for fully discretized equations by Euler (forward and backward) and Crank–Nicolson methods are investigated. The nonlinear term is treated iteratively. A numerical study investigates the convergence and stability of the method. A comparison is also done with some well-known methods and the results reveal the excellence of MLPG7. The convergence of the iterative approach is numerically verified by another illustrative test example. As nonlinear test problems, Allen–Cahn equations are studied.

A Type of Interpolation between Those of Lagrange and Hermite That Uses Nodal Systems Satisfying Some Separation Properties

In this paper, we study a method of polynomial interpolation that lies in-between Lagrange and Hermite methods. The novelty is that we use very general nodal systems on the unit circle as well as on the bounded interval only characterized by a separation property. The way in which we interpolate consists in considering all the nodes for the prescribed values and only half for the derivatives. Firstly, we develop the theory on the unit circle, obtaining the main properties of the nodal polynomials and studying the convergence of the interpolation polynomials corresponding to continuous functions with some kind of modulus of continuity and with general conditions on the prescribed values for half of the derivatives. We complete this first part of the paper with the study of the convergence for smooth functions obtaining the rate of convergence, which is slightly slower than that when equidistributed nodal points are considered. The second part of the paper is devoted to solving a similar problem on the bounded interval by using nodal systems having good properties of separation, generalizing the Chebyshev–Lobatto system, and well related to the nodal systems on the unit circle studied before. We obtain an expression of the interpolation polynomials as well as results about their convergence in the case of continuous functions with a convenient modulus of continuity and, particularly, for differentiable functions. Finally, we present some numerical experiments related to the application of the method with the nodal systems dealt with.

An upwind moving least squares approximation to solve convection-dominated problems: An application in mixed discrete least squares meshfree method

Moving Least Squares (MLS), as a series representation type of approximation, is broadly used in a wide array of meshfree methods. However, using the existing standard form of the MLS causes an unphysical oscillation for the meshfree methods encountering the convection-dominated partial differential equations (PDEs). In this study, several approaches are investigated to enhance the MLS approximation for solving convection-dominated problems. A novel upwind version of MLS approximation called shifted upward MLS (SU-MLS), is presented, which is based on strengthening the effect of upwind nodal points in approximation by wisely adjusting the weight function. Regarding the presented theoretical/numerical investigation, the proposed SU-MLS approximation can yield monotone solutions encountering the convection-dominated PDEs, unlike the existing standard form of MLS. The suggested SU-MLS approximation is, then, utilized in the mixed discrete least squares meshfree (MDLSM) method, rather than the standard MLS which is conventionally used in existing MDLSM. The novel method, which uses SU-MLS, is named upwind MDLSM (UMDLSM). Several numerical examples are investigated, and the results are compared to existing MDLSM. The obtained results indicate that the suggested UMDLSM is remarkably more accurate than the existing MDLSM in convection-dominated PDEs. Furthermore, while the existing MDLSM dramatically suffers from spurious oscillations (wiggling) when the Peclet number is high, the presented UMDLSM can yield monotone and accurate solutions.

Nonlinear statics of three‐dimensional curved geometrically exact beams by a hierarchal quadrature element method

AbstractNonlinear static analyses of three‐dimensional (3D) curved geometrically exact beams are carried out using a hierarchal quadrature element method (HQEM) in this work. The initial value of the rotational quaternions is computed from an initial‐value problem with arc‐length as the “time” variable, so that the quaternions can be differentiated in subsequent computation. The 3D curved geometrically exact beams are first expressed by NURBS and then transformed to be expressed by the hierarchical quadrature bases. The geometrically exact beams are then analyzed by the same hierarchical quadrature bases, which conforms to the isogeometric concept. This procedure of analysis is new. The weak‐form quadrature element method (QEM) is a special case of the hierarchical quadrature element method (HQEM). It is found that the best accuracy may be obtained when the number of integration nodes is one degree less than the nodal points, instead of taking them the same as in the weak‐form QEM. Numerical tests through several examples show that the HQEM can present results with high accuracy using only a few degrees of freedom and is not sensitive to shear locking.

Damping enhancement of nodal modes for stay cables using a single-sided pounding tuned mass damper (SS-PTMD)

Extra long stay cables, owned characteristics of light weight and low damping, may produce large-amplitude vibrations in modes with relatively high frequencies under a moderate wind speed. Installing a transverse fluid viscous damper near the cable anchorage to add maximum damping to the first few cable modes is a traditional method to improve the cable modal damping ratio. However, the installation location of the damper may be coincide with the nodal point of some high vibration modes, and diminishing the damping effect to a large extent. To tackle this nodal mode issue, a single-sided pounding tuned mass damper (SS-PTMD), which exhibits superior control performance over a conventional tuned mass damper (TMD), is adopted to enhance the damping ratio of nodal modes. The coupled equations of motion of a cable equipped with a SS-PTMD are established, and impact force between damper mass and the cable are considered by a impact force model. Free pounding tests are performed to study the pounding behavior with different viscoelastic (VE) material layers and various types of pounding strikers. Numerical simulations are carried out to investigate the damping enhancement and vibration mitigation effect of the SS-PTMD on the cable under various loading cases, including harmonic and simulated turbulent wind excitations. Field performance validations of the SS-PTMD is performed on a cable numbered A10 of the Dongting Lake Bridge. The results from free pounding tests show that the selection of the VE material layers and strikers can greatly affect the pounding behavior of the SS-PTMD. The Numerical simulation of the coupled cable-SS-PTMD system reveals that the SS-PTMD can effectively enhance the damping ratio of the target mode by a SS-PTMD with only 1.08% mass ratio. The numerical results show that SS-PTMD is effective in mitigating the high-oder nodal mode vibration of the cable. Field tests show that after the installation of SS-PTMD, the 2nd-mode modal damping ratio of the cable increases from 0.15% to 1.8%.

Laikmeta komentārs teātra valodā. Latviešu dramaturģija Rīgas Strādnieku teātra repertuārā: modernisma aspekti

The repertoire of the Riga Workers’ Theatre (1926–1934) reflected the trends of the time and leftist progressive ideas. City life as a nodal point of modern reality became inspiration and material for plays, poetry performances, dramatised feuilletons and interludes commenting on current events. The aesthetic programme of the theatre envisaged the creation of a peculiar sovereign artistic style, where the new dramaturgy played an important role. Topical and recently created works by contemporary authors were chosen for the repertoire with an emphasis on the search for novelty. In the first years, while the director was Roberts Dukurs, the dramaturge was Jānis Grots, then Arvīds Grigulis; after this function was taken over by the director Kārlis Dziļleja. The article aims to introduce the main principles of the Riga Workers’ Theatre repertoire policy, focusing on an overview of the contributions of Latvian authors. Rainis, Andrejs Upīts, and Pāvils Gruzna played a dominant role in the ideological decisions of the repertoire. A circle of progressive authors gathered around the theatre, creating a contemporary drama laboratory. Young authors Aleksandrs Čaks, Valdis Grēviņš, Fricis Rokpelnis, Jūlijs Vanags, and others experienced their first works on stage in this theatre. The research object is dramaturgical works and testimonies describing the productions – programme leaflets, reviews, reminiscences, etc. The article discusses innovative trends in drama and the expansion of the concept of dramaturgy to the dynamics of stage set, musical and choreographic action. As a result, the consistently executed repertory policy heralded a new type of drama programme by achieving a synthesis of contemporary content and new visual, musical and choreographic forms. The article concludes that creating innovative drama forms and genre experiments on the Riga Workers’ Theatre stage significantly contributed to the development of Latvian dramaturgy.

Raising the Asymmetric Catalytic Efficiency of Chiral Covalent Organic Frameworks by Tuning the Pore Environment.

Chiral covalent organic frameworks (COFs) hold considerable promise in the realm of heterogeneous asymmetric catalysis. However, fine-tuning the pore environment to enhance both the activity and stereoselectivity of chiral COFs in such applications remains a formidable challenge. In this study, we have successfully designed and synthesized a series of clover-shaped, hydrazone-linked chiral COFs, each with a varying number of accessible chiral pyrrolidine catalytic sites. Remarkably, the catalytic efficiencies of these COFs in the asymmetric aldol reaction between cyclohexanone and 4-nitrobenzaldehyde correlate well with the number of accessible pyrrolidine sites within the frameworks. The COF featuring nearly one pyrrolidine moiety at each nodal point demonstrated excellent reaction yields and enantiomeric excess (ee) values, reaching up to 97 and 83%, respectively. The findings not only underscore the profound impact of a deliberately controlled chiral pore environment on the catalytic efficiencies of COFs but also offer a new perspective for the design and synthesis of advanced chiral COFs for efficient asymmetric catalysis.

Global vibration control of offshore wind turbines with a flexible monopile foundation using a pendulum-tuned mass damper: Risk mitigation and performance incrementation

This study investigates an optimized design approach for a passive-adaptive pendulum-tuned mass damper (PTMD). The PTMD is used to mitigate structural vibrations in offshore wind turbines (OWTs) with flexible monopile foundations considering Pile-Soil Interaction (PSI). The model OWT is based on the 5-MW design proposed by the National Renewable Energy Laboratory (NREL). The PSI incorporates a pile that is modeled as beam–column elements supported by nonlinear springs and accounts for lateral loads (p-y curves) and axial loads (t-z and Q-z curves) at nodal points. Wind and wave spectra estimation, as well as hydrodynamic and aerodynamic load analysis, are performed using a bespoke MATLAB® program operated in conjunction with an ANSYS® 3-D finite element global model. The resultant peak response at the OWT hub was evaluated through power spectral density (PSD) analysis. Optimal design choices for PTMD parameters are obtained via parametric analysis, which assesses the dynamic response in the along and across directions at the hub and stress at the tower base. A systematic representation considers the uncertainties stemming from the geometric and mechanical properties of the tower, environmental loads, and rotating blade dynamics. To address these uncertainties, a Monte Carlo simulation is employed to assess the structural risk via the Performance-Based Wind Engineering (PBWE) framework. Consequently, the probabilistic evaluation of structural response, foundation stresses, and power production assists in the optimal design process of PTMDs that mitigate the global structural vibrations of OWTs.

Software implementation of the algorithm for automatic detection of lineaments and their properties on open-pit dumps

The paper presents an algorithm and a description of its software implementation for detecting lineaments (ground erosions or cracks) in aerial photography images of open-pits. The proposed approach is based on the apparatus of convolutional neural networks based on the semantic classification of binarized images of objects (lineaments), as well as graph theory for determining the geometric location of linearized objects, followed by determining their lengths and areas. Three-channel RGB images of high-resolution aerial photography (pixel 10x10 cm) were used as initial data. The software unit of the model is logically divided into three layers: pre-processing, detection and post-processing. The first level includes preprocessing of input data to form a training sample based on successive transformations of an RGB image into a binary one using the OpenCV library. A neural network of the U-Net type, which includes blocks of the convolutional (Encoder) and scanning parts (Decoder), represents the second level of the information model. At this level, automatic lineament detection (washouts) is implemented. The third level of the model is responsible for calculating the areas and lengths of lineaments. The result of the work of the convolutional neural network is transferred to the input. Lineament area is calculated by summing the total number of points multiplied by the pixel size. The length of the lineaments is computed by linearizing a plane object into a line segmental object with nodal points and then calculating the lengths between them, also relying on the resolution of the original image. The software module can work with input images, with their subsequent resulting merging to the size of the original image.

An innovative simulation algorithm for optimising the cost of communal water supply systems using EPANET

In this work, the EPANET software is used to parametrize the design, simulate and optimise the overall cost of building and running a reliable, sustainable and efficient communal Water Supply System. Considering a model community of forty houses with an average of six occupants per home, the developed optimization algorithm using the simulated annealing heuristics approach minimizes the total cost of continuous water distribution to the community through a system of pipe network in a way that satisfies the critical hydraulic rules and constraints for efficient water distribution. Thus, the controlled variables of the simulated system include volumetric flow, velocity and head loss. To realize the desired goal, the prototyped communal water distribution system was first simulated by water free fall i.e., only gravity feed under a peak demand flow condition. This facilitated the identification and localization of head-loss zones. Subsequently, virtual pump stations of various capacities were optimally introduced as boosters at identified nodal points to overcome critical head losses. The response of the system to varying capacities of the booster pumps was then used to analyse and determine the optimum capacity of the pump. Simulation outcome showed that the optimum least cost design for a sixtyyear system’s life cycle is achieved by using a combination of gravity and 5 hp (3.73 kW) pump with optimum pipe diameter ranging from 60 - 150mm.

‘Hypocrite!’ Affective and argumentative engagement on Twitter, following the Christchurch terrorist attack

This article intervenes in debates about whether public-facing social media enable the rapid spread of hate speech, or whether these platforms can offer valuable opportunities to contest it. Advancing scholarship on ‘networked counter-publics’ and research emphasising the affective dimensions of digital media, we identify three different modes of counter-public contestation that coalesced on Twitter in the immediate aftermath of the Christchurch terrorist attack. Using a combined keyword and hashtag search, our research project sampled 3,099,138 tweets posted on/about the Christchurch attack and its repercussions, between 15 March 2019 and 15 April 2019. First, we examine two hashtags that trended, approaching these as nodal points for the construction of different affective responses to the terrorist attack. Second, we analyse instances where users quote-tweeted the condolences of politicians, rejecting their sentiments, arguing that the sincerity conditions of the Speech Act (condolence) were not met. Here, we focus on the ways that people invoke a discourse of indignation at either the past actions or current character of the politician, to justify rejecting their statements. Our findings illustrate a need to depart from broad narratives about how the affordances of particular social media platforms lend themselves to the circulation or contestation of hate. Instead, we argue, it is important to develop more situated empirical and conceptual approaches to interrogate how specific relationships between affective publics and structures of feeling enable or constrain political possibilities.