Mathematical Modeling Framework Research Articles

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics.

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Mathematical Model and Synthetic Data Generation for Infra-Red Sensors

A key challenge in further improving infrared (IR) sensor capabilities is the development of efficient data pre-processing algorithms. This paper addresses this challenge by providing a mathematical model and synthetic data generation framework for an uncooled IR sensor. The developed model is capable of generating synthetic data for the design of data pre-processing algorithms of uncooled IR sensors. The mathematical model accounts for the physical characteristics of the focal plane array, bolometer readout, optics and the environment. The framework permits the sensor simulation with a range of sensor configurations, pixel defectiveness, non-uniformity and noise parameters.

Modeling Autonomous Vehicles Deployment in a Multilane AV Zone With Mixed Traffic

The advancement of technologies has fast-tracked the deployment of autonomous vehicles (AVs), however, they necessitate the modernization of the existing road infrastructure to meet the technical and safety requirements of AVs. Due to the high cost and prolonged time required for upgrading infrastructure, it is expected that AVs will be introduced gradually into the existing transport network of human-driven vehicles (HVs) either jointly or separately in a special area or zone within that network. In this paper, we propose a mathematical framework for modelling and deployment of multi-lane AV zone in a mixed-user traffic network that takes into account the different route choice decisions of HVs and AVs. The model is used to study two different designs for a multi-lane AV zone, where in Design 1, both lanes are dedicated for AVs inside the AV zone; while in Design 2, one lane is dedicated for AVs, and another lane is for the HV traffic. We then derive an equivalent convex formulation and develop a novel solution method for this complex problem, as well as evaluate and compare the performance of the designs in a realistic large-scale transportation network. Numerical results show that the deployment of a multi-lane AV zone improves network performance in terms of the total system travel time (TSTT). The proposed framework can be used to assist transportation planners and decision-makers to successfully deploy AVs seamlessly with mixed traffic.

The NCC mathematical modeling framework for decision-making of six major cancers

ObjectiveMathematical modeling and simulation is a useful research method to inform decision-making. This article aims to describe the National Cancer Center (NCC) modeling framework and how well it reproduces observed empirical data for six major cancers. MethodsWe developed the NCC modeling framework for six major cancers in China (lung, liver, stomach, colorectal, esophageal, and breast), which simulates the life-histories represented by states among normal, precancerous lesion, stage-specific invasive cancer, and death for six cancers separately. Each NCC simulation model could be illustrated as an integrated framework of 3 modules: a demography module, natural history module, and screening module. Combined with costs and health utilities data, the models could have many detailed outputs for informing decisions, including the harm of screening (e.g., false positives, complications, and overdiagnosis), healthcare costs, and benefits (quality-adjusted life years gained, cancer incidence and mortality, and investment returns). We calibrated the models to Chinese population-based observations on cancer incidence, mortality, and stage distribution. All models are validated by comparing model simulated results to data observed from nationwide cancer registration and a large prospective cohort study. ResultsThe simulated results from the calibrated models consistently match the epidemiological patterns in six major cancer incidence, mortality, and stage distributions in China. Model projected age-specific cancer incidence and mortality were close to the observed data in the national cancer registration. The NCC modeling framework reproduced the cumulative cancer cases and deaths observed in the prospective cohort study at 7.0 and 10.8 years of follow-up. Model estimated net survival rates also consistent with population-based statistics. ConclusionThe NCC modeling framework's ability to reproduce the observed population-level cancer statistics and the cancer cases in a prospective cohort study suggests its results are reliable to inform decision-making related to six major cancers in China.

Unleashing the Potentials of Quantum Probability Theory for Customer Experience Analytics

In information systems research, the advantages of Customer Experience (CX) and its contribution to organizations are largely recognized. The CX analytics evaluate how customers perceive products, ranging from their functional usage to their cognitive states regarding the product, such as emotions, sentiment, and satisfaction. The most recent research in psychology reveals that cognition analytics research based on Classical Probability Theory (CPT) and statistical learning, which is used to evaluate people’s cognitive states, is limited due to their reliance on rational decision-making. However, the cognitive attitudes of customers are characterized by uncertainty and entanglement, resulting in irrational decision-making bias. What is captured by traditional CPT-based data science in the context of cognition aspects of CX analytics is only a small portion of what should be captured. Current CX analytics efforts fall far short of their full potential. In this paper, we set a novel research direction for CX analytics by Quantum Probability Theory (QPT). QPT-based analytics have been introduced recently in psychology research and reveal better cognition assessment under uncertainty, with a high level of irrational behavior. Adopting recent advances in the psychology domain, this paper develops a vision and sets a research agenda for expanding the application of CX analytics by QPT to overcome CPT shortcomings, identifies research areas that contribute to the vision, and proposes elements of a future research agenda. To stimulate debate and research QPT-CX analytics, we attempt a preliminary characterization of the novel method by introducing a QPT-based rich mathematical framework for CX cognitive modeling based on quantum superposition, Bloch sphere, and Hilbert space. We demonstrate the implementation of the QPT-CX model by the use case of customers’ emotional motivator assessments while implementing quantum vector space with a set of mathematical axioms for CX analytics. Finally, we outline the key advantages of quantum CX over classical by supporting theoretical proof for each key.

Local Grey Predictor Based on Cubic Polynomial Realization for Market Clearing Price Prediction

With the development of restructured power markets, the profit-making competitive business environment has emerged. With the help of different advanced technologies, generating companies are taking decisions regarding trading electricity with imperfect information about marketing operating conditions. The forecasting of the market clearing price (MCP) is a potential issue in these markets. Early information on the MCP can be a proven beneficial tool for accumulating profit. In this work, a local grey prediction model based on a cubic polynomial function is presented to estimate the MCP with the help of historical data. The mathematical framework of this grey model was established and evaluated for different market conditions and databases. The comparison between traditional grey models and some advanced grey models reveals that the proposed model yields accurate results.

Deciphering longitudinal optical-density measurements to guide clinical dosing regimen design: A model-based approach

BackgroundModel-based analysis of longitudinal optical density measurements from a bacterial suspension exposed to antibiotics has been proposed as a potentially efficient and effective method for extracting useful information to improve the individualized design of treatments for bacterial infections. To that end, the authors developed in previous work a mathematical modeling framework that can use such measurements for design of effective dosing regimens. ObjectivesHere we further explore ways to extract information from longitudinal optical density measurements to predict bactericidal efficacy of clinically relevant antibiotic exposures. MethodsLongitudinal optical density measurements were collected in an automated instrument where Acinetobacter baumannii, ATCC BAA747, was exposed to ceftazidime concentrations of 1, 4, 16, 64, and 256 mg/L and to ceftazidime/amikacin concentrations of 1/0.5, 4/2, 16/8, 64/32, and 256/128 (mg/L)/(mg/L) over 20 h. Calibrated conversion of measurements produced total (both live and dead) bacterial cell concentration data (CFU/mL equivalent) over time. Model-based data analysis predicted the bactericidal efficacy of ceftazidime and of ceftazidime/amikacin (at ratio 2:1) for periodic injection every 8 h and subsequent exponential decline with half-life of 2.5 h. Predictions were experimentally tested in an in vitro hollow-fiber infection model, using peak concentrations of 60 and 150 mg/L for injected ceftazidime and of 40/20 (mg/L)/(mg/L) for injected ceftazidime/amikacin. ResultsModel-based analysis predicted low (<62%) confidence in clinically relevant suppression of the bacterial population by periodic injections of ceftazidime alone, even at high peak concentrations. Conversely, analysis predicted high (>95%) confidence in bacterial suppression by periodic injections of ceftazidime/amikacin combinations at a wide range of peak concentrations ratioed at 2:1. Both predictions were experimentally confirmed in an in vitro hollow fiber infection model, where ceftazidime was periodically injected at peak concentrations 60 and 150 mg/L (with predicted suppression confidence 38% and 59%, respectively) and a combination of ceftazidime/amikacin was periodically injected at peak concentrations 40/20 (mg/L)/(mg/L) (with predicted suppression confidence 98%). ConclusionsThe paper highlights the potential of clinicians using the proposed mathematical framework to determine the utility of different antibiotics to suppress a patient-specific isolate. Additional studies will be needed to consolidate and expand the utility of the proposed method.

A rubric for assessing mathematical modelling problems in a scientific-engineering context

Abstract Mathematics modelling is a vital competency for students of all ages. In this study, we aim to fill the research gap about valid and reliable tools for assessing and grading mathematical modeling problems, particularly those reflecting multiple steps of the modelling cycle. We present in this paper the design of a reliable and valid assessment tool aimed at gauging the level of mathematical modelling associated with real-world modeling problems in a scientific-engineering context. The study defines and bases the central modelling processes on the proficiency levels identified in PISA Mathematics. A two-dimensional rubric was developed, reflecting the combined assessment of the type and level of a modelling process. We identified criteria that enable a clear comparison and differentiation among the different levels across each of the modelling processes. These criteria allow for concrete theoretical definitions for the various modelling processes, introducing a well-defined mathematical modelling framework from a didactical viewpoint, which can potentially contribute to promoting modelling competencies or the understanding of modelling by teachers and students. Theoretical, methodological and practical implications are discussed.

Epigenetic factor competition reshapes the EMT landscape

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene-regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as gene-regulatory networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks. In such models, epigenetic factors are usually proposed to act on the chromatin regions directly involved in the expression of relevant genes. However, it has been well-established that these factors operate globally and compete with each other for targets genome-wide. Therefore, a perturbation of the activity of a regulator can redistribute epigenetic marks across the genome and modulate the levels of competing regulators. In this paper, we propose a conceptual and mathematical modeling framework that incorporates both local and global competition effects between antagonistic epigenetic regulators, in addition to local transcription factors, and show the counterintuitive consequences of such interactions. We apply our approach to recent experimental findings on the epithelial-mesenchymal transition (EMT). We show that it can explain the puzzling experimental data, as well as provide verifiable predictions.

An open-access data set of pig skin anatomy and physiology for modelling purposes.

The use of animal as opposed to human skin for in vitro permeation testing (IVPT) is an alternative, which can reduce logistical and economic issues. However, this surrogate also has ethical considerations and may not provide an accurate estimation of dermal absorption in humans due to physiological differences. The current project aimed to provide a detailed repository for the anatomical and physiological parameters of porcine skin, with the aim of parametrizing the Multi-phase Multi-layer Mechanistic Dermal Absorption (MPML MechDermA) Model in the Simcyp Simulator. The MPML MechDermA Model is a physiologically based pharmacokinetic (PBPK) model that accounts for the physiology and geometry of skin in a mechanistic mathematical modelling framework. The database provided herein contains information on 14 parameters related to porcine skin anatomy and physiology, namely, skin surface pH, number of stratum corneum (SC) layers, SC thickness, corneocyte thickness, corneocyte dimensions (length and width), volume fraction of water in corneocyte (where SC is divided into four parts with different water contents), intercellular lipid thickness, viable epidermis thickness, dermis thickness, hair follicle and hair shaft diameter, hair follicle depth and hair follicle density. The collected parameters can be used to parameterize PBPK models, which could be further utilized to bridge the gap between animal and human studies with interspecies extrapolation or to predict dermatokinetic properties typically assessed in IVPT experiments. Database URL: https://data.mendeley.com/datasets/mwz9xv4cpd/1

Penalaran Matematis: Pembiasaan Soal High Order Thinking Pada Siswa Usia Sekolah Dasar

The purpose of the article is to create a mathematical reasoning modeling framework through working on high order thinking questions for elementary school students. The modeling cycle (formulating, applying, interpreting, and evaluating) is a central aspect of the conception of mathematical reasoning for students for the sake of mathematical literacy. Formulating is an individual's ability to recognize and identify opportunities to use mathematics and then provide a mathematical structure for problems presented in several contextual forms. Applying is an individual's ability to apply concepts, facts, procedures, and mathematical reasoning to solve mathematically formulated problems in order to obtain mathematical conclusions. Interpreting and evaluating (interpret and evaluate) is the individual's ability to reflect on mathematical solutions, results or conclusions and interpret them into the context of real life problems. This is a literature study, the data was collecting using literature studies on scientific journal articles and news about mathematical reasoning, high order thinking, and numeracy. The modeling cycle is recommended for teaching mathematics in elementary school through series of problem solving stages in questions with higher order thinking skill concept.

Optimal deployment of autonomous buses into a transit service network

Autonomous vehicles empowered by emerging automation technologies are highly anticipated to be introduced into public transit service operations in the future mobility system. Considering the low acceptance rate of the new service with autonomous buses when it is initially put into practice, it is not ideal to make a “one-off” deployment to replace all the service lines with autonomous bus services. Rather, the service operator is to determine an optimal plan for the deployment of autonomous buses onto different service lines in multiple stages. This paper proposes a multi-stage mathematical modeling framework to optimize the deployment strategy in which conventional buses are sequentially replaced by autonomous buses. More specifically, the model decides when (at which planning stage) and where (on which service line in the network) the deployment of autonomous buses should be conducted. Passengers’ acceptance attitudes towards autonomous buses are explicitly considered in their transit routing choices. To forecast the evolution of the passengers’ adoption rate of the autonomous bus service, a diffusion model is applied. The proposed multi-stage planning model framework, which is indeed a mixed-integer nonlinear program, is to determine the optimal deployment strategy that minimizes the total travel cost during the planning horizon. A two-phase solution method that combines a searching algorithm and a double projection method is proposed to solve the model. Finally, numerical studies are conducted to test the validity of the modeling framework and solution method. The impacts of passengers’ adoption rate and other parameters on the deployment strategy are illustrated.

Modelling inflammatory biomarker dynamics in a human lipopolysaccharide (LPS) challenge study using delay differential equations.

Clinical studies in healthy volunteers challenged with lipopolysaccharide (LPS), a constituent of the cell wall of Gram-negative bacteria, represent a key model to characterize the Toll-like receptor 4 (TLR4)-mediated inflammatory response. Here, we developed a mathematical modelling framework to quantitatively characterize the dynamics and inter-individual variability of multiple inflammatory biomarkers in healthy volunteer LPS challenge studies. Data from previously reported LPS challenge studies were used, which included individual-level time-course data for tumour necrosis factor α (TNF-α), interleukin 6 (IL-6), interleukin 8 (IL-8) and C-reactive protein (CRP). A one-compartment model with first-order elimination was used to capture the LPS kinetics. The relationships between LPS and inflammatory markers was characterized using indirect response (IDR) models. Delay differential equations were applied to quantify the delays in biomarker response profiles. For LPS kinetics, our estimates of clearance and volume of distribution were 35.7Lh-1 and 6.35L, respectively. Our model adequately captured the dynamics of multiple inflammatory biomarkers. The time delay for the secretion of TNF-α, IL-6 and IL-8 were estimated to be 0.924, 1.46 and 1.48 h, respectively. A second IDR model was used to describe the induced changes of CRP in relation to IL-6, with a delayed time of 4.2h. The quantitative models developed in this study can be used to inform design of clinical LPS challenge studies and may help to translate preclinical LPS challenge studies to humans.

Optimization of service frequency and vehicle size for automated bus systems with crowding externalities and travel time stochasticity

Public transport is considered as one of the most suitable candidates to benefit from autonomous driving technologies. In this research, we develop a mathematical modeling framework to optimize service frequency and vehicle size for automated bus systems, while accounting for both user and operator costs. We explicitly consider travel time stochasticity, time-dependent passenger flows, vehicle capacity limitations (extra waiting time due to denied boarding), and in-vehicle discomfort externalities for both sitting and standing passengers at a microscopic level. We attempt to provide a thorough assessment of the service and cost implications of the deployment of automated buses. Hence, a broad range of experiments are simulated by combining different deployment cases: (i) vehicle technology (human-driven or automated vehicles), (ii) travel time assumptions (deterministic or stochastic travel times), and (iii) crowding externalities (considering or ignoring in-vehicle crowding costs). The model applicability is assessed on two real-world bus corridors in Regensburg (Germany) and Santiago (Chile). Results show that, with crowding externalities, optimal vehicle size is increased at a similar rate for both human-driven and automated bus services, whereas optimal service frequency is increased at a higher rate for automated buses. Thus, under optimal levels of supply, automated vehicles are operated with lower occupancy levels than human-driven vehicles, increasing the quality of service. Besides, the deployment of automated bus systems can significantly alleviate or eliminate denied boardings. The effects of automation on travel time volatility and dwell time regularity are studied. The consideration of stochastic travel times increases optimal frequencies at a higher rate for automated services relative to human-driven vehicles. Interestingly, we find that even though the operator benefits from automation are more pronounced in high-income countries (due to a greater potential for human driving cost savings), the final outcome is counterbalanced by the actual public transport demand level, because large user cost savings from automation are reachable in crowded routes even in situations in which labor costs are lower (as in developing countries).

Patient-specific molecular response dynamics can predict the possibility of relapse during the second treatment-free remission attempt in chronic myelogenous leukemia

In chronic myelogenous leukemia (CML), treatment-free remission (TFR) is defined as maintaining a major molecular response (MMR) without a tyrosine kinase inhibitor (TKI), such as imatinib (IM). Several studies have investigated the safety of the first TFR (TFR1) attempt and suggested recommendation guidelines for such an attempt. However, the plausibility and predictive factors for a second TFR (TFR2) have yet to be reported.The present study included 21 patients in chronic myeloid leukemia who participated in twice repeated treatment stop attempts. We develop a mathematical model to analyze and explain the outcomes of TFR2. Our mathematical model framework can explain patient-specific molecular response dynamics. Fitting the model to longitudinal BCR-ABL1 transcripts from the patients generated patient-specific parameters. Binary tree decision analyses of the model parameters suggested a model based predictive binary classification factor that separated patients into low- and high-risk groups of TFR2 attempts with an overall accuracy of 76.2% (sensitivity of 81.1% and specificity of 69.9%). The low-risk group maintained a median TFR2 of 28.2 months, while the high-risk group relapsed at a median time of 3.25 months. Further, our model predicted a patient-specific optimal IM treatment duration before the second IM stop that could achieve the desired TFR2 (e.g., 5 years).

Measuring fractal dynamics of FECG signals to determine the complexity of fetal heart rate

In this research, we study the fetal heart rate from abdominal signals using multi-fractal spectra and fractal analysis. We use the Abdominal and Direct Fetal Electrocardiogram Database contains multichannel fetal electrocardiogram (FECG) recordings obtained from 5 different women in labor, between 38 and 41 weeks of gestation. We apply autocorrelation or power spectral densities (PSD) analysis on these five FECG recordings to estimate the exponent from realizations of these processes and to find out if the signal of interest exhibits a power-law PSD. We perform multi-fractal analysis to discover whether some type of power-law scaling exists for various statistical moments at different scales of these FECG signals. We plot the multi-fractal spectra of this database to compare the width of the scaling exponent for each spectrum. A quantitative analysis commonly known as the Fractal Dimension (FD) using the Higuchi algorithm has been carried out to illustrate the fractal complexity of input signals. Our finding shows that the fractal geometry can be used as a mathematical model and computational framework to further analysis and classification of clinical database. Moreover, it can be considered as a framework to compare the complexity of FECG signals and a useful tool to differentiate between their patterns.

Long-term coexistence of two invasive vespid wasps in NW Patagonia (Argentina).

In Patagonia (Argentina) two non-native vespid wasps became established in the last decades. Vespula germanica was first detected in 1980, while V. vulgaris arrived some 30years later. Both species can have a strong negative impact on agro-industrial economic activities, the natural environment, and outdoor human activities. Biological invasions may be influenced negatively by the degree of interaction with the resident native community and alien species already present. The sequential arrival and coexistence of Vespula wasps in Argentina for several years allows us to understand key questions of invasion ecology. Additionally, recognizing the outcome of the invasion by vespids in Patagonia, a region lacking native social wasps, may help plan species-focused mitigation and control strategies. We explored the role of competition in terms of invasion success, and the strategies that promote coexistence. Two possible scenarios, using niche overlap indices and isocline equations, were proposed to determine competition coefficients. Using a simple mathematical modeling framework, based on field collected data, we show that food resources do not play a central role in competitive interaction. The competition coefficients obtained from the equations were different from those inferred from the overlap indices (0.53 and 0.54-0.076 and 0.197, respectively). Together, these findings suggest that no matter the arrival order, V. vulgaris, always reaches higher densities than V. germanica when both species invade new regions. Our work contributes to further our understanding on the worldwide invasion processes deployed by these two eusocial insects.

Abstract 2742: A biology-based, mathematical model to predict the response of recurrent glioblastoma to treatment with 186Re-labeled nanoliposomes

Abstract Introduction: 186Re-nanoliposomes (RNL) are a theranostic that emits a therapeutic payload of ionizing beta radiation, and a gamma photon to be measured with SPECT. The RNL is delivered via convection-enhanced delivery, resulting in a highly localized distribution around the glioma that produces up to a 30-fold increase in maximum tolerable dose. RNL provides a continuous source of low dose rate irradiation, until the particles are cleared biologically or decay. The goal of this study is to evaluate the accuracy of a patient calibrated reaction-diffusion equation for predicting the growth and response of recurrent glioblastoma multiforme (GBM) following treatment with RNL. Methods: Multi-parametric images were collected from patients (n=10) receiving RNL treatment, consisting of pre-treatment and follow-up MRIs (Day 0, 28*, 56, 112*) and SPECT/CTs acquired at the middle and end of infusion, and 24-, 112-, and 192-hours post-infusion. For each time point, tumor segmentations and cell count maps are computed using contrast enhanced and diffusion weighted MRI, respectively. The spatio-temporal response to RNL is modeled using a biology-informed reaction-diffusion model describing tumor cell proliferation, invasion, and radiation induced death. Key model parameters related to the RNL activity are populated through a quantification of the SPECT time course. The remaining model parameters related to diffusivity, proliferation, and death rate are calibrated via the Levenberg-Marquardt algorithm for each individual patient, and then used to forecast growth. Calibrations are performed in two different scenarios, first to all imaging time points to assess the model capabilities (Scenario 1), and then without the last acquired MRI, which is set aside to evaluate prediction accuracy (Scenario 2). Error will be assessed at the global (Dice similarity coefficient and percent error in total cell number) and local (concordance correlation coefficient or CCC) levels for both scenarios. *Patients are scanned on day 28 or day 112 at a minimum, potentially both (n=5) Results: Scenario 1 calibrations produced on average, Dice=0.92, CCC=0.69, and total cell percent error = 10.2%, validating usage of the current model formulation. Scenario 2 calibrations show high prediction success on a global scale, mean Dice=0.78, mean total cell percent error =23%, but resulted in poor local accuracy, mean CCC=0.21. Discussion &amp; conclusion: The mathematical model and processing framework can predict the spatiotemporal evolution of recurrent GBM after treatment with RNL. Ongoing efforts include validating the methodology on a larger cohort and further model selection to improve predictive capabilities. Citation Format: Chase Christenson, Chengyue Wu, David A. Hormuth, Shiliang Huang, Andrew Brenner, Thomas E. Yankeelov. A biology-based, mathematical model to predict the response of recurrent glioblastoma to treatment with 186Re-labeled nanoliposomes [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2742.

A Modeling Framework for Coupling Plasticity with Species Diffusion

This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework is important to a wide variety of problems ranging from Li-ion batteries, moisture diffusion in cementitious materials, hydrogen diffusion in metals, to consolidation of soils under severe loading-unloading regimes. The mathematical model incorporates experimental observations reported in the literature on how (elastic and plastic) material properties change because of the presence and transport of a chemical species. Also, the model accounts for one-way (transport affects the deformation but not vice versa) and two-way couplings between deformation and transport subproblems. The resulting coupled equations are not amenable to analytical solutions; so, we present a robust computational framework for obtaining numerical solutions. Given that popular numerical formulations do not produce nonnegative solutions, the computational framework uses an optimized-based nonnegative formulation that respects physical constraints (e.g., nonnegative concentrations). For completeness, we will also show the effect and propagation of the negative concentrations, often produced by contemporary transport solvers, into the overall predictions of deformation and concentration fields. Notably, anisotropy of the diffusion process exacerbates these unphysical violations. Using representative numerical examples, we will discuss how the concentration field affects plastic deformations of a degrading solid. Based on these numerical examples, we also discuss how plastic zones spread because of material degradation. To illustrate how the proposed computational framework performs, we report various performance metrics such as optimization iterations and time-to-solution.

A hierarchical performance evaluation approach for the sustainability of smart grid

PurposeThe purpose of this study is to establish a hierarchy of critical success factors to develop a framework for evaluating the performance of smart grids from a sustainability perspective.Design/methodology/approachThe fuzzy analytical hierarchy process is used in this study to assess and determine the relative weight of economic, operational and environmental criteria. At the same time, the evidential reasoning algorithm is used to determine the belief degree of expert’s opinion, and the expected utility theory for the crisp value of success factors in performance estimation.FindingsThe finding reveals that success factors associated with the economic criteria receive significantly more attention from the expert group. Sensitivity analysis indicates the ranking of consumer satisfaction remains stable no matter how criteria weights are changed, which verifies the robustness and effectiveness of the proposed model and evaluation results.Originality/valueThe study presents a solid mathematical framework for collaborative system modeling and systematic analysis. Managers and stakeholders may use the proposed technique as a flexible tool to improve the energy system’s resiliency in a systematic way.