Graphical Procedure Research Articles

Diffusion coefficient calculation using the Boltzmann-Matano methodwith a graphical approach for understanding annealed Copper-Zinc couples

This article delves into transport phenomena, essential in science and engineering research, emphasizing Matano's Interface as a key element in diffusion studies. The primary goal is to elucidate a graphical procedure for approaching Matano's Interface within diffusion couples, aiming to calculate diffusion coefficients across various compositions. The comprehensive exploration of the Boltzmann-Matano method, particularly focusing on concentration-dependent diffusion coefficients, is accentuated. Acknowledging the historical context of Ludwig Boltzmann and Matano, the article highlights the practical application of their methodologies, notably in an annealed copper-zinc couple. The graphical determination of the Boltzmann-Matano interface proves crucial in understanding diffusion dynamics. The article successfully integrates theoretical understanding with practical insights, contributing to the broader field of transport phenomena research in science and engineering.

Computer-assisted regional-residual gravity anomaly separation with regularized first- and second-order derivatives

The regional-residual separation of gravity anomalies in crustal and mineral exploration was a graphical-based procedure before the advent of fast digital computers and the need for more efficient algorithms to process large data sets. However, since requiring the supervision of an experienced interpreter, the results, once obtained with graphical procedures, are often accepted as second to none in producing anomalies with geologic significance. Numerical methods based on spectral filtering and robust polynomial fitting have worked in many scenarios but seem not fully effective in replicating in algorithms the kind of results once obtained with interpreter-assisted graphical methods. We develop a computer-assisted regional residual separation (CARRS) procedure implemented by a set of short MATLAB scripts; in many aspects, CARRS simulates the operations of former graphical methods but requires few decisions and minor handwork from the interpreter. CARRS applies robust polynomial fitting to points with a low horizontal gradient and a vertical second-order derivative; thus, selecting fitting points as a real interpreter would do with graphical approaches in outlining the regional field. A regularized procedure is used to calculate the stable first- and second-order derivatives. Companion MATLAB codes allow for the replication of our results and further exploration with different threshold levels to identify flat domain regions. CARRS is illustrated with airborne gravity data CPRM-1123, freely available to download. A data window of the residual field is used to analyze the distribution of cassiterite deposits in greisen zones of the Paleoproterozoic Velho Guilherme granites in the Amazon Craton, as their distribution appears in the observed gravity anomaly and its corresponding residual field.

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

STABILITY ROBUSTNESS OF CONTROL SYSTEMS OF MULTIROTOR UNMANNED AERIAL VEHICLES

Multirotor unmanned aerial vehicles (UAVs) are broadly used in various military and civilian areas and tasks. In real flights of the multirotor UAVs, certain unexpected situations may occur, which can lead to improper functionality and even failures of elements or devices of the UAV’s control system. In some cases, this can even lead to the complete collapse of the UAV. Therefore, the safety of UAV flights is nowadays of prime importance. A method of analysis of the stability robustness of the UAV’s control systems with respect to the parameters multiplicative uncertainties (or perturbations), including possible efficiency degradation of DC motors, is proposed in the paper. Stability robustness is determined by a simple graphical procedure on the complex plane of the Nyquist or Nichols hodographs of the control system’s separate channels. That procedure is quite similar to the well-known classical feedback control procedure of determining the peak gain of the single-input, single-output closed-loop control system by the Nyquist hodograph of the open-loop system. A numerical example illustrating the proposed method is given.

Evaluating the incompleteness magnitude using an unbiased estimate of the b value

SUMMARY The evaluation of the b value of the Gutenberg–Richter (GR) law, for a sample composed of n earthquakes, presents a systematic positive bias δb which is proportional to 1/n . In this study, we show how to incorporate in δb the bias introduced by deviations from the GR law. More precisely we show that δb is proportional to the square of the variability coefficient CV, defined as the ratio between the standard deviation of the magnitude distribution and its mean value. When the magnitude distribution follows the GR law CV = 1 and this allows us to introduce a new graphical procedure, based on the dependence of b on n, which allows us to identify the incompleteness magnitude mc as the threshold magnitude leading to CV = 1. The method is tested on synthetic catalogues and it is applied to estimate mc in Southern California, Japan and New Zealand.

Analysis of tracking characteristics of a heliostat field using a graphical ray tracing procedure

The tracking requirements of all heliostats in a field are not the same, and they vary according to day, time, and latitude. In this work, a graphical ray tracing (GRT) based model is developed and demonstrated with two-axis Azimuth-Elevation (AE) and Spinning-Elevation (SE) tracking techniques. The procedure is simple and obviates the complex rotation-matrices formulation reported in the previous literature. Using the GRT, a new Center-Oriented Spinning-Elevation (COSE) tracking technique is proposed and demonstrated in which, instead of at the target, heliostats are pointed towards the on-field center-point of the tower. Tracking based on this co-ordinate system results in a substantial reduction in rotations of tracking motors and parasitic-energy of heliostats. Motion analysis of eight heliostats placed at different on-field locations and distances from the tower are conducted, and their tracking characteristics are explained in detail with respect to time, latitude, and tracking modes. The effect of on-field position and distance is presented with fast-tracking requirements and reflected mirror images on the receiver plane. The COSE method obtains a better shape of the reflected-image with less aberration on the receiver plane than SE and AE methods. The analysis performed in this work addresses the trade-off between tracking speed and cost while designing a tracking system for heliostat field.

The ZX-calculus as a language for topological quantum computation

Unitary fusion categories formalise the algebraic theory of topological quantum computation. These categories come naturally enriched in a subcategory of the category of Hilbert spaces, and by looking at this subcategory, one can identify a collection of generators for implementing quantum computation. We represent such generators for the Fibonacci and Ising models, namely the encoding of qubits and the associated braid group representations, with the ZX-calculus and show that in both cases, the Yang–Baxter equation is directly connected to an important rule in the complete ZX-calculus known as the P-rule, which enables one to interchange the phase gates defined with respect to complementary bases. In the Ising case, this reduces to a familiar rule relating two distinct Euler decompositions of the Hadamard gate as Z- and X-phase gates, whereas in the Fibonacci case, we give a previously unconsidered exact solution of the P-rule involving the Golden ratio. We demonstrate the utility of these representations by giving graphical derivations of the single-qubit braid equations for Fibonacci anyons and the single- and two-qubit braid equations for Ising anyons. We furthermore present a fully graphical procedure for simulating and simplifying braids with the ZX-representation of Fibonacci anyons.

Optimizing Parameters for an Electrical Car Employing Vehicle Dynamics Simulation Program

At the Faculty of Engineering of the University of Debrecen we have dealt with the design and construction of electric prototype race cars for more than a decade. With a focus on more conscious design and racing we developed a vehicle dynamics simulation program, which can be used to generate the dynamics functions of the cars from their technical characteristics and data. In this publication, we deal with the optimization of the technical parameters of the above-mentioned cars for various competition tasks using our simulation program. This is a completely new field of application of the used optimization methods. This concept and idea can effectively help student teams all over the world to prepare for various domestic and international competitions. One of the applied methods is a graphic procedure, the other one is the widely used “adaptive simulated annealing” (ASA). After a brief description of the simulation program, the applied optimization methods and developed MATLAB codes for them are described. Finally, to demonstrate the effectiveness of the methods, we optimize the parameters of a prototype race car for different competition tasks and present the obtained results.

Python programs to apply regularized derivatives in the magnetic tilt derivative and gradient intensity data processing: A graphical procedure to choose the regularization parameter

The Tikhonov regularization parameter is a key parameter controlling the smoothness degree and oscillations of a regularized unknown solution. Usual methods to determine a proper parameter (L-curve or the discrepancy principle, for example) are not readily applicable to the evaluation of regularized derivatives, since this formulation does not make explicit a set of model parameters that are necessary to implement these methods. We develop a procedure for the determination of the regularization parameter based on the graphical construction of a characteristic “staircase” function associated with the L2-norm of the regularized derivatives for a set of trial regularization parameters. This function is independent of model parameters and presents a smooth and monotonic variation. The regularization parameters at the upper step (low values) of the ''staircase'' function provide equivalent results to the non-regularized derivative, the parameters at the lower step (high values) leading to over-smoothed derivatives. For the evaluated data sets, the proper regularization parameter is located in the slope connecting these two flat end-members of the staircase curve, thus balancing noise amplification against the amplitude loss in the transformed fields. A set of Python programs are presented to evaluate the regularization procedure in a well-known synthetic model composed of multiple (bulk and elongated) magnetic sources. This numerical approach also is applied in gridded aeromagnetic data covering high-grade metamorphic terrains of the Anápolis-Itauçu Complex in the Brasília Fold Belt central portion of Tocantins Province, central Brazil, characterized by multiple magnetic lineaments with different directions and intersections which are associated with shear zones, geologic faults, and intrusive bodies. The results obtained from the regularization procedure show efficiency in improving the maps of filtered fields, better tracking the continuity of magnetic lineaments and general geological trends. The results from the application in the Brasília Fold Belt enhance the importance and broader coverage of the Pirineus Zone of High Strain.

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.

Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation

The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material. We introduce complex stochastic models which may substitute expensive laboratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the interaction is between pairs of orientations for neighbouring grains in the tessellation. We discuss parameter estimation and model comparison methods based on maximum pseudolikelihood as well as graphical procedures for model checking using simulations. Our methodology is applied for analysing a dataset representing a nickel–titanium shape memory alloy.

Graphical modeling of discontinuous stress field for RC deep beams under uniform load

AbstractThe fanning compression stress pattern in RC deep beams under uniform load presents a challenge to formulating the configuration of strut‐and‐tie model (STM). To this end, this paper proposes an alternative method for creating a graphical discontinuous stress field model (DSFM) to fill up the whole beam continuum. It comprises a certain number of trapezoidal stress‐bands with varying bandwidths, and their stress values can be calculated based on force equilibrium conditions. Several stress subfields are defined through a certain stress combination from several directions. The DSFM is implementable for both service limit state (SLS) and ultimate limit state (ULS) in that its configuration is primarily oriented by elastic stress field and only a limited plastic redistribution is allowed for plastic failure. The graphical procedure of DSFM is demonstrated and examined by a test deep beam example, which shows that the predictions are fairly in good agreement with the test results.

An Extended Framework of Multiple Testing in Group Sequential Design.

Here, we consider testing multiple hypotheses in group sequential trials. A graphical multiple test procedure was proposed for group sequential trials using weighted Bonferroni test. In this paper, we extend the framework for the graph-based group sequential procedure by applying a modified weighted Simes test. The proposed procedure preserves the familywise error rate. Simulations are conducted to evaluate the performances of the proposed procedure. The proposed procedures are also illustrated with a numerical example.

Graphic Transfer Matrix Method for Kinetostatic and Dynamic Analyses of Compliant Mechanisms

Abstract Kinetostatic and dynamic analyses of compliant mechanisms with complex configurations continue to be an attractive issue for obtaining a process-concise and result-accurate solution. In this paper, the transfer matrix method (TMM) is improved for a unified linear kinetostatics and dynamic modeling of compliant mechanisms with complex serial-parallel configurations in an oriented graphic way. In detail, the transfer matrices of typical building blocks commonly used in compliant mechanisms are summarized and derived. Then, a graphic transfer matrix modeling procedure capturing both the kinetostatics and dynamics of general compliant mechanisms is introduced. The displacement amplification ratio, input/output stiffness, parasitic error, natural frequencies, and frequency response of a typical compliant microgripper and a planar parallel three-degrees-of-freedom (3DOF) nanopositioner are calculated with such a graphic transfer matrix method. The advantages of the proposed modeling method lie in its convenience and uniformity in formulating both the kinetostatic and dynamic behaviors of a class of compliant mechanisms with distributed and lumped compliances in a transfer matrix manner, which has minimal DOF and is easily programmed.

The Performance Evaluation of Nine Methods for the Estimation of Weibull Distribution Parameters

In this paper, a report on the different methods for estimation of the parameter of the Weibull 2-parameter distribution is presented. The nine approaches were compared in terms of their fits using the statistical criteria (analysis of variance (ANOVA), model of' selection criterion (MSC), Coefficient of Determination (CD), Correlation coefficient (R) and Akaike Information Criterion (AIC)) to select the best method. The study revealed that mean rank is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method significantly outperformed other methods based on the MSC, CD, R and AIC. The values for the parameters in the Weibull 3-parameter were 1.316, 105.425 mm/h and 0.293 for α, β and λ respectively. The values of MSC, CD AIC and R were 1.853 and 1.453, 0.860 and 0.802, 211.891 and 295.978, and 0.927 and 0.895 for Weibull 2 and 3 – parameters respectively. It was concluded that mean rank, symmetric, Lysen and Moment methods are the best based on the values of MSC, CD and R. Care must be taken in selecting MLM, graphical and least square methods for Weibull distribution parameters determined based on the lower values of MSC, CD and R as well as higher values of AIC.

A Procedure for the Squaring of a Circle (of Any Radius)

This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm2. This result was a clear demonstration that not only is the construction valid for the squaring of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.

ROBUSTNESS ANALYSIS OF UAVS’ CONTROL SYSTEMS IN CASE OF MOTORS’ PARTIAL EFFICIENCY DEGRADATION

Multirotor unmanned aerial vehicles (UAVs) are widely used in military tasks, as well as in various civilian areas such as agriculture, search and rescue operations, detection of fires in forests, traffic monitoring, etc. In real flights of the UAVs some unexpected situations may occur bringing to failures of various elements or devices of the UAV’s control system. This, in turn, can lead to the crush and complete collapse of the entire vehicle. First of all, it concerns the DC motors and propellers, which, as opposed to electronic devises and sensors, cannot be duplicated. A method of analysis of robustness of UAV’s control systems with respect to possible partial efficiency degradation of motors is proposed in the paper. The ultimately allowable efficiency degradation is determined by a simple graphical procedure on the complex plane of the Nyquist hodographs of the system’s separate channels. A numerical example illustrating the proposed method of analysis of the UAV’s control system robustness is given.

Critical Limit of Boron in Soil and Cauliflower

Boron plays an important role in crop nutrition. Cauliflower expresses its sensitivity towards boron application which ultimately decides the potential of crop yield and the quality of curds. In this study, we presented the assessment of the critical level of soil boron concentration by graphical and statistical procedures using cauliflower as a test crop. Thirty (30) soil samples collected from three rice growing sub-division of Imphal-west district were used for conducting the pot experiment. The experiment was laid out in a Completely Randomized Design with six treatments replicated thrice. The treatments setting were as follows: T0= Control, T1= 0.5 mg B kg-1 soil, T2= 1 mg B kg-1 soil, T3= 1.5 mg B kg-1 soil, T4= 2 mg B kg-1 soil and T5= 2.5 mg B kg-1 soil. The plants were harvested at curd formation stage and used for estimation of the critical limits of boron. The critical level of boron concentration in soil and plant was found to be 0.46 and 24.50 mg kg-1, respectively, by graphical procedure, whereas by statistical procedure it was found to be 0.45 and 24.59 mg kg-1 in soil and plant, respectively. It was evident that critical limits worked out by both the procedures, i.e., graphically and statistically, were closely related. These values may be used to predict the response of cauliflower to the applied boron. The range between the deficiency and toxicity for boron in plants is little, therefore utmost care in management should be taken.

DIFFERENTIAL ROLES OF COVID-19-RELATED STRESSORS IN MENTAL HEALTH PROBLEMS: A NETWORK APPROACH

Abstract COVID-19-related stress is heterogeneous and associated with increased mental health conditions in older adults. This study is to investigate relationships between different stressors and how different stressors may increase risks for mental health conditions through a network approach. A telephone survey was conducted among 4,921 older adults (age≥60) from April to June 2022 during the biggest community outbreak of COVID-19 in Hong Kong. The validated 8-item COVID-19-Related Stress Scale (CSS-old) (Cronbach’s α: 0.91) was used to investigate the different stressor for older people in Hong Hong. Respondents were screened for depression using the Patient Health Questionnaire-2 (PHQ-2), anxiety using the Generalized Anxiety Disorder 2-item (GAD-2), and stressors with the CSS-old, 4708 responded to all questions. A regularized partial correlation network via graphical LASSO procedure was computed to analyze the relationship between 8 stressors; a directed acyclic graph (DAG) via a Bayesian hill-climbing algorithm was generated from CSS-old and comorbidity network with PHQ-2 and GAD-2 items. Network analyses identified CSS-old item 6 (families or friends infected), item 3 (daily life interrupted), item 5 (fear of infection affecting the family), and item 8 (worry for community’s health) as the core stressors. DAG analysis found a key triggering role for item 1 (suspension of community services), and the activation of the mental health problems occurred through item 1, which bridged the COVID-19-related stress and mental health problems. These findings suggested that providing support for families with COVID-19 patients and alternative services during community service suspension may reduce mental health problems risks.

Robust stability testing function for a complex interval family of fractional-order polynomials

The robust stability of a family of interval fractional-order systems with complex coefficients is investigated in this study. The concept of “a family of interval fractional-order systems with complex coefficients” means that the characteristic function of a control system can be of both commensurate and non-commensurate orders, the coefficients of the characteristic function can be uncertain parameters, and may be complex numbers. At first, a simple graphical procedure is presented for robust stability analysis. The “robust stability testing function” is then extended to look at the robust conditions. To the best of the authors’ knowledge, no auxiliary function for analyzing the robust stability of the systems under investigation has been introduced until now. Moreover, lower and upper frequency bounds are provided which are useful to improve the computational efficiency of testing the robust stability conditions. Eventually, to verify the results, analytical examples and numerical simulations are provided.