Classical Direct Method Research Articles

Integrating the probe and singular sources methods

Abstract The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods.

A new modified direct method for determining the mode I delamination traction-separation law

A new equation was developed for the crack-tip separation in the double cantilever beam (DCB) specimen, which has been standardised for mode I delamination of composites. The very simple closed-form equation is based on a pseudo-elastic beam model and on the effective crack concept. Moreover, it only requires the common load–displacement data up to crack initiation and easy to obtain elastic moduli. Strain-energy release rate versus crack-tip separation curves can then be differentiated for obtaining the tractions, as in the classical direct method. Numerical results for piecewise linear traction-separation laws (TSL) showed good accuracy of strain-energy release rate versus crack-tip separation curves predicted. Application to two carbon/epoxy materials gave very promising TSL results, including cohesive strengths similar to transverse tensile strengths and post-peak steep traction decreases.

Resilient based consensus of fractional-order delayed Multi-Agent Systems in Riemann-Liouville Sense

In this paper, in Riemann-Liouville sense, delayed multi-agent system of fractional-order is being considered, in which we consider corresponding topology is weighted graph. To make controller design more practical, it is assumed that the controller is not implemented as it is and we consider the case, when there is disturbance in controller, which is assumed to be bounded. By applying algebraic graph theory and classical Lyapunov direct method, some algebraic criteria are provided and for analysing consensus, a new method is used. Corresponding Lyapunov function of first order can be considered is major reason for suggested access. For showing validity of our approach, some effective examples are also provided.

A topic-aware classifier based on a hybrid quantum-classical model

In the era of Large Language Models, there is still potential for improvement in current Natural Language Processing (NLP) methods in terms of verifiability and consistency. NLP classical approaches are computationally expensive due to their high-power consumption, computing power, and storage requirements. Another computationally efficient approach to NLP is categorical quantum mechanics, which combines grammatical structure and individual word meaning to deduce the sentence meaning. As both quantum theory and natural language use vector space to describe states which are more efficient on quantum hardware, QNLP models can achieve up to quadratic speedup over classical direct calculation methods. In recent years, there is significant progress in utilizing quantum features such as superposition and entanglement to represent linguistic meaning on quantum hardware. Earlier research work has already demonstrated QNLP’s potential quantum advantage in terms of speeding up search, enhancing classification tasks’ accuracy and providing an exponentially large quantum state space in which complex linguistic structures can be efficiently embedded. In this work, a QNLP model is used to determine if two sentences are related to the same topic or not. By comparing our QNLP model to a classical tensor network-based one, our model improved training accuracy by up to 45% and validation accuracy by 35%, respectively. The QNLP model convergence is also studied when varying: first, the problem size, second, parametrized quantum circuits used for model’s training, and last, the backend quantum simulator noise model. The experimental results show that strongly entangled ansatz designs result in fastest model convergence.

Structure determination of a low-crystallinity covalent organic framework by three-dimensional electron diffraction

Covalent organic frameworks (COFs) have been attracting intense research due to their permanent porosity, designable architecture, and high stability. However, COFs are challenging to crystallize and their synthesis often results in tiny crystal sizes and low crystallinities, which hinders an unambiguous structure determination. Herein, we demonstrate that the structure of low-crystallinity COF Py-1P nanocrystals can be solved by coupling three-dimensional electron diffraction (3DED) with simulated annealing (SA). The resulting model is comparable to that obtained from high-crystallinity samples by dual-space method. Moreover, for low-resolution 3DED data, the model obtained by SA shows a better framework than those provided by classic direct method, dual-space method, and charge flipping. We further simulate data with different resolutions to understand the reliability of SA under different crystal quality conditions. The successful determination of Py-1P structure by SA compared to other methods provides new knowledge for using 3DED to analyze low-crystallinity and nanosized materials.

Assessment of magnetoelastic resonance parameters retrieval for sensor applications

Magnetoelastic resonance sensors have been widely used for several sensing applications, as their resonance behavior is very sensitive to different external factors and they can be operated remotely. Nevertheless, under some working conditions, such as when the sensor signal is low, has considerable noise, or the medium viscosity causes damping of the signal, the accuracy in obtaining the parameters that characterize the resonance response of these sensors by direct methods can decrease. The aim of this work is to improve the performance of magnetoelastic sensors through the use of numerical fittings of the resonance curves to obtain accurately the resonance parameters used for detection. The capability of these numerical fittings to retrieve the parameters when signals present different levels of noise is evaluated, and the accuracy of this fitting method is compared with the precision of classical direct methods.

Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.

Comparison of Classical methods and Chromogen Media for Detection of Stool Colonisation by Carbapenem-resistant Enterobacteriaceae

Abstract Objectives: We aimed to compare classical methods and chromogenic media to detect carbapenem-resistant Enterobacteriaceae (CRE) colonization among hospitalized patients and determine the risk factors causing infection in colonized patients. Methods: Between January and August 2017, 100 patients over the age of 18 who were hospitalized in the Reanimation Intensive Care Unit and the Trauma Emergency Intensive Care Unit of a university hospital were examined. From the first day of intensive care unit (ICU) admission, rectal swabs were collected once every week and were tested for the presence of CRE by using the classical method defined by the Centers for Disease Control and Prevention (CDC), ChromID CARBA chromogenic medium, and direct inoculation into MacConkey agar plates. In addition, MIC values for imipenem, ertapenem, meropenem and colistin were determined by using the Etest. Results: Rectal BDE carriage was detected by at least one method in 46 (46%) of 100 patients included in the study. Sensitivity and specificity values of the CDC classical method, direct MacConkey inoculation, and ChromID CARBA medium in the first 24 hours were found as 78%-42%, 87%-80%, and 91%-98%, respectively. Sensitivity and specificity values of these methods after 72 hours were determined as 78%-100%, 87%-100%, and 91%-100%, respectively. Conclusion: We observed that, although the ChromID CARBA method performed better than classical CDC and direct MacConkey inoculation methods, direct MacConkey inoculation can still be employed, especially in areas with limited resources. Keywords: carbapenem, carbapenemase, rectal colonization

Gnielinski’s correlation and a modern temperature-oscillation method for measuring heat transfer coefficients

The heat transfer coeffcient is one of the most important parameters in the design of apparatuses in which convective heat transport takes place. Classical direct methods based on determining basic thermal quantities can be used for measuring heat transfer coeffcients. Another option is to measure concentrations, electric current or other quantities that can be transformed to thermal quantities using the analogy between heat and mass transport. The temperature-oscillation method is less frequently used, although the theoretical basis of the method dates back to 1997, and although the method has the major advantage that the heat transfer coeffcients can be measured without making any contact with the heat transfer surface. In the temperatureoscillation method, the heat transfer surface is exposed to an oscillating heat flux, and the temperature response on this surface can be measured by a contactless method (e.g. infra-red thermography). The heat transfercoeffcients can be determined on the basis of mathematical relations between the oscillating heat flux and the temperature response. However, the method depends on an appropriate method for processing the measured data when it is necessary to correct some conditions that are not included in the mathematical model. This paper evaluates the impact of processing the experimental data on the resulting heat transfer coeffcients in one of the basic geometrical configurations – the flow of a liquid in a pipe with a circular cross section. In this paper, we present the results of a comparison of real experiments based on the temperature oscillation method and numerical modeling of the heat transfer in this geometry, using the ANSYS CFD commercial system.

Detection of Individual Replacements in a Long-Lived Bird Species, the Bonelli's Eagle (Aquila fasciata), Using Three Noninvasive Methods

ABSTRACT Accurate estimations of adult mortality are essential for understanding population dynamics and achieving efficient management actions that are directed toward long-lived species. Several noninvasive methods may be used to monitor endangered long-lived birds like raptors, but their performance in real-world scenarios remains poorly studied. We used eight Bonelli's Eagle (Aquila fasciata) breeding pairs (1) to compare the efficiency of direct observations with binoculars and telescopes (2004–2016), camera trapping (2012–2016), and feather genetic analysis (2004–2015) for detecting and identifying individuals over time, (2) to conduct a cost-benefit analysis of methods, and (3) to evaluate the accuracy of the direct observation method for estimating survival by comparing it with camera trapping and feather analysis. Both the feather genetic analysis and camera trapping approaches allowed us to successfully identify individuals and to detect replacements that we did not notice during direct observations. The classic direct observation method overestimated adult survival, which could hamper an accurate understanding of the demographic dynamics of this population. Feather analysis gave a low detection rate of individuals (47%), probably due to difficulties in finding feathers in the rugged habitat of this species. However, identification success at the individual level with this method was 96%. Remote camera surveys had both a high detection rate (100%) and identification success (93%). Given that costs associated with camera surveys were lower than the costs of genetic procedures, we concluded that camera trapping is the most efficient indirect method to assess adult survival in this and other raptors with external features that make individual identification possible. However, because no method showed complete efficiency, genotyping of feathers collected at the end of the breeding season could be a useful additional method, especially when camera trapping is not possible or when it fails.

Some investigations on convergence of GMRES in solving BEM equations for slender beam structures

The boundary element method (BEM) has remarkable advantages in dimension reduction and higher accuracy, but the classical direct method (like Gauss elimination) is not efficient for large scale problems and not suitable for the implementation of fast algorithms like Fast-Multipole Method (FMM) or methods base on the hierarchical matrices. Alternatively, some iterative methods for nonsymmetrical systems of linear equations, such as the Generalized Minimum Residual Method (GMRES), has much improvement in convergence and computational efficiency and is well compatible with fast algorithms. However, in our recent research, we found that the convergence of conventional GMRES is slow for thin-walled structure. For example, for the slender beam problem, the convergence is obviously decreased with the increase of the slenderness ratio of the beam. In this paper, by taking the slender beam as an example, we investigate the convergence and efficiency of GMRES method dealing with BEM equations. Some influences about slenderness ratio, the behavior of the orthogonalization process and restart strategy, and preconditioning process are under consideration. A new preconditioner is proposed based on the geometry of the slender beam, and numerical results have shown that it can bring much improvement in convergence and computational efficiency.

A new weighted fraction Monte Carlo method for particle coagulation

PurposeThe purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.Design/methodology/approachThe weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.FindingsThree typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.Originality ValueStochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

ОЦЕНКА ЭФФЕКТИВНОСТИ СТРУКТУРНОГО КОМПАКТНО-МАТРИЧНОГО МЕТОДА РАСЧЕТА КОЭФФИЦИЕНТА КОМПАКТНОСТИ

The article examines the efficiency of the structural compact-matrix numerical method in comparison with the classical direct numerical method for calculating the spatial packing density of the simplest hexagonal lattice. The theoretical results of a comparative analysis of the considered numerical meth-ods, as well as a computational experiment, carried out to quantitatively assess their effectiveness, are presented.

STABILITY ANALYSIS IN BANACH SPACES FOR A GENERAL ADDITIVE FUNCTIONAL EQUATION

In this paper, we present the Hyers-Ulam stability of generalized additive functional equation in Banach spaces and stability results have been obtained by a classical direct method by various general control functions.

Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay

<p style='text-indent:20px;'>We consider the 3D Navier-Stokes-Voigt equations in a bounded domain with unbounded variable delay. We study the stability of stationary solutions by the classical direct method, and by an appropriate Lyapunov functional. We also give a sufficient condition of parameters for the polynomial stability of the stationary solution in a special case of unbounded variable delay. Finally, when the condition for polynomial stability is not satisfied, we stabilize the stationary by using the finite Fourier modes and by internal feedback control with a support large enough.</p>

Fuzzy logic direct torque/power control for a self-excited induction generator driven by a variable wind speed turbine

This paper presents a new direct fuzzy control scheme for a decentralized wind power generation system with a wide operation range of wind speed variations. The proposed scheme makes use of direct fuzzy torque and power control laws to improve the performance of the system and more particularly the quality of energy inserted into the electrical grid. The direct fuzzy torque control law is used to generate the control signal of the converter on the generator side in order to extract the maximum power available at the turbine and also to maintain the stator flux of the machine at an acceptable level while the direct fuzzy power control law of the converter is used on the grid side to obtain a power efficiency close to unity. A comparison of simulation results between the proposed control method and the classical direct control method found in the literature, shows that the proposed control method provides better performance by improving trajectory tracking as well as robustness against variations in the internal parameters of the asynchronous generator (rotor resistance and stator resistance). It also ensures a supply of quality electrical energy into the electrical grid.

Consensus of fractional-order delayed multi-agent systems in Riemann–Liouville sense

Fractional-order delayed multi-agent systems (FDMASs) in Riemann–Liouville sense are considered, where the corresponding topology is a weighted digraph. A new method is adopted to analyze consensus and some algebraic criteria are provided by applying classical Lyapunov direct method and algebraic graph theory. The main merit of our proposed approach is that the first-order derivative of the corresponding Lyapunov function can be taken. Two illustrative examples are provided to further show the validity of our approach.

Survey of derivative-free optimization

<p style='text-indent:20px;'>In this survey paper we present an overview of derivative-free optimization, including basic concepts, theories, derivative-free methods and some applications. To date, there are mainly three classes of derivative-free methods and we concentrate on two of them, they are direct search methods and model-based methods. In this paper, we first focus on unconstrained optimization problems and review some classical direct search methods and model-based methods in turn for these problems. Then, we survey a number of derivative-free approaches for problems with constraints, including an algorithm we proposed for spherical optimization recently.

A new ordinary differential equation for the evaluation of the frequency-domain Green function

Clément (2013) derived a second order ordinary differential equation (ODE) satisfied by the free-surface Green function in the frequency domain. Since then, similar ODEs for the gradient of the Green function have been developed. Unfortunately, all these ODEs degenerate at zero frequency. Therefore, it is not possible to initialize the numerical solution of these ODEs from this zero frequency. Alternative methods based on the shifting of the initial condition to frequencies strictly greater than zero have then been developed.The present paper describes an alternative approach to address this issue. It involves a new function which is the solution of a modified ODE which can be solved from the zero frequency.Finally, comparisons with evaluations of the Green function using the classical direct integration method are provided. They show that the new ODE can provide accurate estimates of the Green function.

Phaseless inverse source scattering problem: Phase retrieval, uniqueness and direct sampling methods

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the underlying sources. Furthermore, the phaseless far field pattern is also invariant if the source is multiplied by any complex number with modulus one. Therefore, the source can not be uniquely determined, even the multi-frequency phaseless far field patterns are considered. By adding a reference point source into the model, we propose a simple and stable phase retrieval method and establish several uniqueness results with phaseless far field data. We proceed to introduce a novel direct sampling method for shape and location reconstruction of the source by using broadband sparse phaseless data directly. We also propose a combination method with the novel phase retrieval algorithm and the classical direct sampling methods with phased data. Numerical examples in two dimensions are also presented to demonstrate their feasibility and effectiveness.