Stochastic Modeling Techniques Research Articles

Integration of Geological Model and Numerical Simulation Technique to Characterize the Remaining Oil of Fractured Biogenic Limestone Reservoirs

AbstractFine geological modeling leads to accurate reservoirs numerical simulations. Fractured biogenic limestone has abundant storage spaces and flow paths to accumulate oil and gas. The complexity and diversity of fractured biogenic limestone also lead to challenges in accurately characterizing its pore volume and remaining oil. This investigation aimed to enhance the understanding of fractured biotite reservoir properties via geological modeling. Numerical simulations were used to characterize the remaining oil during the late stage of field development. Considering the differences in porosity and permeability between fractures and matrix, a facies-controlled stochastic modeling technique was used to establish a dual-porosity and dual-permeability (DPDP) model for numerical simulation. Core information, logging data, and multiple seismic attributes were combined to guide low-level sequence fault interpretation for tectonic refinement. Based on classified seismic inversion, sedimentary phases were reconstructed. A discrete fracture network (DFN) model was obtained based on fracture occurrences and density models. The optimized discrete adjoint (ODA) algorithm was utilized to calibrate model parameters. The findings revealed that dense tectonic fractures develop in thick biogenic limestone areas. Combined with advanced reservoir simulation technology, these findings suggest that areas of thicker biogenic limestone were consistent with areas of higher fracture matrix conductivity multipliers. The remaining oil distribution patterns were investigated, and to deploy new wells was guided. Therefore, it is essential to better understand the tectonic characteristics of fractured biogenic limestone reservoirs and their remaining oil distribution patterns by integrating multiple sources of information and mastering advanced reservoir simulation technology for oilfield development.

Application of simulation and machine learning in supply chain management: A synthesis of the literature using the Sim-ML literature classification framework

Stochastic modeling techniques, such as discrete-event and agent-based simulation, are widely used in supply chain management (SCM) for capturing real-world uncertainties. Over the last decade, data-driven approaches like machine learning (ML) have also gained prominence in SCM, employing methods such as supervised learning (SL), unsupervised learning (UL), and reinforcement learning (RL). As supply chains grow in complexity, hybrid models combining simulation (Sim) and ML are becoming increasingly common, and the field stands to gain from a structured review of this literature. Towards this, we developed the Sim-ML Literature Classification Framework, which includes a hierarchical taxonomy comprising five SC criteria, 22 Sim-ML classes and over 75 Sim-ML subclasses. We applied this framework to synthesize 99 papers, revealing significant diversity in how Sim-ML models are used to address supply chain challenges. Key findings include the recognition of the breadth of study objectives, identifying various forms of model hybridization achieved by combining discrete/continuous simulation techniques with SL, UL, and RL approaches, and the data flow mechanisms such as sequential and feedback methods employed by the simulation and ML elements of the hybrid model. Our findings also identify some gaps in the literature; for example, optimization is rarely incorporated into Sim-ML models. Also, most studies present Sim-ML models for addressing problems in general supply chains, likely due to the lack of access to industrial data. The review also highlights that Industry 4.0 technologies, such as digital twins and blockchain, are underrepresented in current research, as are topics like sustainability and transportation. These gaps suggest significant opportunities for future research. We provide guidelines for practitioners on applying Sim-ML models to manage supply chain drivers, mitigate the impact of disruptions, and integrate emerging technologies. Our review serves as a valuable resource for researchers, practitioners, and students interested in leveraging Sim-ML approaches in SCM.

Limited role of present-day onshore freshwater recharge in the emplacement of offshore freshened groundwater in the Canterbury Bight, New Zealand

ABSTRACT Offshore freshened groundwater (OFG) represents a significant, yet underexplored, component of the global freshwater system as it is found across various continental margins. In this study, a 3-D geological and groundwater model was developed for the Canterbury Plains and Bight (New Zealand) to assess the role of present-day onshore recharge in the emplacement of OFG. Topographic and bathymetric, seismic reflection and well data have been integrated to construct an onshore-offshore geological model. The facies property distribution and associated hydrodynamic parameters were determined using stochastic modelling techniques. The geological reconstruction was imported within a variable density groundwater model. Simulations, under transient regime, were run until equilibrium conditions between the involved aquifer portion and the adjacent ocean have been reached. Our results show that the geological model accurately captures the stratigraphic and sedimentary features of the area, and that onshore recharge at present contributes to OFG emplacement up to 15 km from the coast, which is equivalent to 25% of its maximum extent. Onshore recharge during sea-level lowstands is therefore the dominant OFG emplacement mechanism in the Canterbury Bight.

Enhancing community resilience to urban heat waves: A simulation-based approach for volunteer management and shelter selection

This study proposes a novel approach to enhancing urban resilience and emergency management practices in the face of heatwave events, often exacerbated by the urban heat island effect. Recognizing the limitations of traditional government-led responses in shelter allocation—characterized by high costs, logistical challenges, and a lack of adaptability—this paper introduces an innovative framework that integrates community-based volunteer efforts with advanced simulation and stochastic modelling techniques. The primary objective is to optimize the allocation of resources and volunteers to improve the efficiency and cost-effectiveness of heatwave response mechanisms. Utilizing Data Envelopment Analysis (DEA), the research identifies and enhances resource and volunteer distribution strategies, paving the way for more effective emergency services. A case study conducted in Blacktown City, Western Sydney, serves to demonstrate the practical application and implications of these strategies, underscoring the necessity for a paradigm shift towards more adaptable, volunteer-focused, and resource-efficient approaches in mitigating the impact of climate-change-induced heat waves on vulnerable urban populations. The anticipated outcomes include measurable improvements in response times, cost reductions, and enhanced volunteer mobilization efficiency.

Influence of sedimentary architecture on static connectivity and geothermal doublet performance (Mezőberény, SE Hungary)

Although the Pannonian Basin in Hungary boasts significant geothermal potential, most geothermal wells in the region suffer from reinjection issues. The aim of this study is to examine the impact of the sedimentary architecture of a paralic lacustrine succession on the static connectivity of a geothermal aquifer. This problem was examined for a case-study geothermal doublet drilled in Mezőberény, southeast Hungary, which experienced injectivity problems shortly after commencing operations in 2012, ultimately leading to shut-in of the wells. A characterization of the architecture of the deltaic aquifer has been undertaken through a novel workflow that combines sedimentological and sequence stratigraphic analysis of the well-doublet and stochastic 3D modelling techniques to assess the likely static connectivity between the production and injection wells. Planform dimension of aquifer-forming mouth-bar elements and fluvial channel bodies were estimated from geological analogues, selected based on the thickness values of such sedimentary bodies interpreted on the gamma-ray logs of the well doublet and nearby hydrocarbon wells. In total five mouth-bar and two fluvial channel input geometry groups were selected, and fifty object-based realizations were constructed to analyse the static connectivity of different geological scenarios. The internal lithology of mouth-bar and fluvial-channel elements were modelled by sequential indicator simulations (ten realizations). Results of connected volume analysis indicate that the sandstone content of the aquifer is located within vertically segmented fluvial-channel and mouth-bar elements separated by mud-prone prodelta and lower delta-front deposits. This architectural configuration, in combination with low net-sandstone content suggests limited connectivity between the wells. Across the set of stochastic realizations, the volume of sandstone connecting the injection and production wells is ∼4% of the total aquifer volume, on average. Results of this study shows that simplified reservoir models can lead to over-estimation of connectivity of geothermal doublets. The proposed workflow combines sedimentological analysis and 3D modelling supported by geological analogues to predict sandstone reservoir connectivity of deltaic geothermal reservoirs. The described workflow can be carried out in target areas using existing boreholes to assist borehole planning.

A two‐stage reliable computational scheme for stochastic unsteady mixed convection flow of Casson nanofluid

AbstractResearchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler‐Maruyama method for stochastic modeling, representing a stochastic version of the third‐order explicit‐implicit scheme. For the deterministic model, the scheme is third‐order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy‐related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.

On the stochastic threshold of the COVID-19 epidemic model incorporating jump perturbations

This work delves into the intricate realm of epidemic modeling under the influence of unpredictable surroundings. By harnessing the power of white noise and Lévy noise, we construct a robust framework to capture the behavioral characteristics of the COVID-19 epidemic amidst erratic changes in the external environment. To enhance our comprehension of the intricate dynamics of the coronavirus, we conducted an investigation using a stochastic SIQS epidemic model that incorporates a dedicated compartment to represent populations under quarantine. Thanks to stochastic modeling techniques, we account for the inherent randomness in the transmission process and provide insights into the potential variations and uncertainties associated with the progression of the epidemic. Specifically, we show that the asymptotic behavior of our model is perfectly governed by two thresholds, Rσ,J and Rσ,J′. That is to say, if Rσ,J<1, the disease will be removed from the population, while it will persist if Rσ,J′>1. Our highlight lies in obtaining the necessary and sufficient conditions for extinction in the absence of jump noise, namely Rσ,0=Rσ,0′. This means that our sufficient conditions for extinction for the jump case are also almost necessary. Finally, we present a set of computational simulations to validate our theoretical findings, supporting the results developed throughout this article. Overall, this research contributes to our understanding of the COVID-19 pandemic and its impact on the global population.

Three-Dimensional Geological Modeling of Coal Reservoirs and Analysis of Sensitivity Factors for Combined Mining Capacity

Due to the large non-homogeneity of coal reservoirs, there is a large uncertainty about the extent of the impact on coal bed methane production capacity. The Hanchengbei Block has the problems of early exploration, less available production data, and large variations in developed production capacity within a single well group during test production. Therefore, how to use the existing data to analyze the geological factors affecting the development of coalbed methane in the Hanchengbei Block is particularly important. In this paper, based on the coal seam properties and production characteristics of the Hanchengbei Block, a three-dimensional geological model of the area was meticulously constructed using Petrel 2015 modeling software. Through the utilization of stochastic modeling techniques, reservoir attributes were visualized in three dimensions, and probability distribution functions as well as confidence intervals for different geological parameters were derived through geological statistics. Building upon this foundation, a dual-layer geological model incorporating multiple factors was established using Comet3.0 numerical simulation software. Monte Carlo simulation methods were then employed to simulate the effects of various geological parameters on gas production, yielding corresponding simulation results. Through normalization processes, parameter sensitivity was analyzed to determine the primary controlling factors influencing production capacity. The results show that the thickness of the No. 5 coal seam in the Hanchengbei Block is mainly distributed in the range of 1.35–6.89 m; the gas content is 10.28–15.52 m3/t; and the permeability is 0.014–0.048 mD. Under their joint influence, the average gas production of Hanchengbei Block is between 310–720 m3/d. The main factors affecting the capacity of Hanchengbei Block are the thickness and gas content of the coal seam. This study can provide a basis for the subsequent optimization of favorable areas, the formulation of drainage systems, and the design and optimization of development well networks.

Development of stochastic deep learning model for the prediction of construction noise

Construction noise is an occupational noise that is potentially harmful, and it usually originates from machinery in construction sites. The impact of construction noise on the health and safety of construction workers is one of the main concerns in the industry. Prolonged noise exposure duration will cause physiological, physical, psychological damage, and negatively affect the working performance of the workers as well. Furthermore, the adverse impacts arising from construction noise may jeopardize public welfare, particularly for those who live nearby the construction site. Therefore, this research aims to develop a Stochastic Deep Learning (SDL) noise prediction model by integrating stochastic modelling and deep learning techniques. Stochastic modelling is applied in this study to generate a set of simulated randomized data based on several parameters as the input for the deep learning model. The deep learning model is trained with the input from stochastic modelling to predict the noise levels emitted from the construction site. The predictive performance of the deep learning model will be assessed with several statistical measures such as absolute difference, mean absolute difference and root mean square deviation. Ten case studies are conducted to validate the reliability and accuracy of the SDL noise prediction model. The SDL model showed high accuracy of prediction results with an average absolute difference of less than 1.2 A-weighted decibels (dBA) among the case studies as compared to the measurement. The reliability of the results from the prediction model is high. In conclusion, the SDL model is established and provided a promising outcome with satisfactory predictive performance. Finally, further development of the model would be worthwhile to fully exploit the potential of the SDL noise prediction model in construction industries as a planning, managerial and monitoring tool.

Stochastic modeling of porous sound absorbing materials using homogenization method and machine learning

This research introduces a novel approach to investigate porous sound absorbing materials using stochastic modeling techniques. The study employs the homogenization method and machine learning to predict the acoustic properties of porous materials. The homogenization method simplifies the analysis of microstructural properties in porous materials, while machine learning is a data analysis technique that utilizes algorithms to learn from data and make predictions. By integrating these methods, this study quantitatively assesses the impact of microscopic structural randomness on sound absorption properties. The study assumes that microstructural parameters are random variables and calculates the sound absorption coefficient through homogenization method. This dataset serves as input for machine learning. A Gaussian process regression model is developed using the dataset to evaluate the distribution of the sound absorption coefficient via the Gauss-Hermite quadrature method. The study implements Bayesian optimization, utilizing the variance of the resulting probability distribution as the acquisition function, to adaptively update the dataset. By iteratively performing these processes, the probability distribution of the sound absorption coefficient can be predicted efficiently and with high accuracy.

Assessing safety functionalities in the design and validation of driving automation

This paper aims to contribute to the comprehensive and systematic safety assessment of Automated Driving Systems (ADSs) by identifying unknown hazardous areas of operation. The current methodologies employed in this domain typically involve estimating the distributions of situational variables based on human-centered field test, crash databases, or expert knowledge of critical values. However, due to the lack of a-priori knowledge regarding the influential factors, their critical ranges, and their distributions, these approaches may not be entirely suitable for the assessment of emerging automated driving technologies. To deal with this challenging problem, here we propose a testing methodology incorporating realistic yet unobserved driving conditions, distinguished by numerous situational variables, so to encompass unknown unsafe conditions comprehensively. Our methodology utilizes stochastic simulation and uncertainty modeling techniques to account for the variability of realistic driving conditions and their impact on ADSs' performances. By doing so, we aim to identify unsafe operational regions and triggering conditions that can lead to hazardous behaviors, thus improving the development and safety of automated driving functions. For our purposes, the Latin Hypercube Sampling technique and the recently proposed PAWN density-based sensitivity analysis method are employed. We apply this methodology for the first time in the specific field of ADSs design and validation, using an exemplificative use case. We discuss and compare the results obtained from our approach with those obtained from a traditional approach.

Micro Computed Tomography based stochastic design and flow analysis of dry fiber preforms manufactured by automated fiber placement

The effective design of channels in dry tape preforms is crucial for achieving desired preform permeability for successful resin injection for composites manufacturing using Automated Fiber Placement (AFP) process. Achieving target gaps and their locations in the AFP layup is extremely challenging. This work investigates the correlation between the spatial variability of the preforms and the in-plane permeability using an X-ray Computed Tomography (XCT) based characterization framework. The tomographic images of two different dry carbon tape preforms with different tape widths were used to generate realistic and XCT based stochastic models to be used for numerical permeability predictions. The variability in the tape placement by the robotic head and its effect on preform permeability was also examined through stochastic geometric modeling of the laid preform. A benchmark transient permeability measurement set-up was utilized to obtain experimental in-plane preform permeability through 2D radial mold filling. The in-plane numerical permeability values showed significant scatter, with a coefficient of variance of 75%–130%, which deviated from the experimental measurements by approximately one order of magnitude. These findings strongly re-affirm that the experimental permeability measurement technique based on transient mold filling of dry fiber AFP preforms is complex however, the XCT based stochastic modeling technique is an effective way to estimate the permeability of dry fiber AFP preforms virtually.

Clustering Approach for the Efficient Solution of Multiscale Stochastic Programming Problems: Application to Energy Hub Design and Operation under Uncertainty

The management of the supply chain for enterprise-wide operations generally consists of strategic, tactical, and operational decision stages dependent on one another and affecting various time scales. Their integration usually leads to multiscale models that are computationally intractable. The design and operation of energy hubs faces similar challenges. Renewable energies are challenging to model due to the high level of intermittency and uncertainty. The multiscale (i.e., planning and scheduling) energy hub systems that incorporate renewable energy resources become more challenging to model due to an integration of the multiscale and high level of intermittency associated with renewable energy. In this work, a mixed-integer programming (MILP) superstructure is proposed for clustering shape-based time series data featuring multiple attributes using a multi-objective optimization approach. Additionally, a data-driven statistical method is used to represent the intermittent behavior of uncertain renewable energy data. According to these methods, the design and operation of an energy hub with hydrogen storage was reformulated following a two-stage stochastic modeling technique. The main outcomes of this study are formulating a stochastic energy hub optimization model which comprehensively considers the design and operation planning, energy storage system, and uncertainties of DRERs, and proposing an efficient size reduction approach for large-sized multiple attributes demand data. The case study results show that normal clustering is closer to the optimal case (full scale model) compared with sequence clustering. In addition, there is an improvement in the objective function value using the stochastic approach instead of the deterministic. The present clustering algorithm features many unique characteristics that gives it advantages over other clustering approach and the straightforward statistical approach used to represent intermittent energy, and it can be easily incorporated into various distributed energy systems.

A comparative analysis of (s, Q) and (s, S) ordering policies in a queueing-inventory system with stock-dependent arrival and queue-dependent service process

This article deals with a Markovian queuing-inventory system (MQIS) under the stochastic modeling technique. The arrival stream of this system is dependent on the present stock level at an instant. Meanwhile, the system focuses on reducing the waiting time of a unit by assuming a queue-dependent service policy (QDSP). The system consists of an infinite waiting hall to receive an arriving unit. The MQIS assumes that no unit of arrival is allowed when the stock level of the system is empty. The discussion of this MQIS runs over the two types of ordering principles named 1) (s, Q) 2) (s, S). According to both ordering principles, the assumed arrival and service patterns have been considered separately and classified as Model-I (M-I) and Model-II (M-II) respectively. The steady state of the system for both M-I and M-II is analysed and resolved under the Neuts matrix-geometric technique. The system performance measures of the system are also computed. The expected cost function of both M-I and M-II are constructed as well. Further, the necessary numerical illustrations are provided and distinguished for M-I and M-II to explore the proposed model. This paper finds the optimum ordering policy to execute the stock-dependent arrival and queue-dependent service strategies.

Experiences With Deep Learning Enhanced Steering Mechanisms for Debugging of Fundamental Cloud Services

Cloud architecture blueprints or reference architectures allow the reuse of existing knowledge and best practices when creating new cloud native solutions. Therefore, debugging reference architecture candidates (or their new versions) is an extremely crucial but tedious and time-consuming task due to the deployment of complex services in typical multi-tenant and non-deterministic environments. During the debugging/testing/maintenance scenarios, we might be able to achieve greater levels of test coverage (and eventually improved reliability) by modelling and verifying at least their most fundamental building blocks. The main objective of our work is to integrate the stochastic modelling and verification techniques based on deep learning methods into the debugging cycle in order to handle large state spaces more efficiently, i.e. by steering the process of traversing state space towards suspicious situations that may result in potential bugs in the actual system with smart steering during the traversal. For this purpose, our presented and illustrated approach combines (among others) Continuous Time Markov Chain modelling (CTMC) techniques with deep learning methods including autoencoder, Long Short-Term Memory (LSTM) and Graph Neural Network (GNN) models. Our experiences are summarized with widespread cloud design patterns including load balancing and service mesh topologies.

On Performance Evaluation of Inertial Navigation Systems: The Case of Stochastic Calibration

In this work we address the problem of rigorously evaluating the performances of an inertial navigation system during its design phase in presence of multiple alternative choices. We introduce a framework based on Monte-Carlo simulations in which a standard extended Kalman filter is coupled with realistic and user-configurable noise generation mechanisms to recover a reference trajectory from noisy measurements. The evaluation of several statistical metrics of the solution, aggregated over hundreds of simulated realizations, provides reasonable estimates of the expected performances of the system in real-world conditions. This framework allows the user to make a choice between alternative setups. To show the generality of our approach, we consider an example application to the problem of stochastic calibration. Two competing stochastic modeling techniques, namely, the widely popular Allan variance linear regression, and the emerging generalised method of wavelet moments, are rigorously compared in terms of the framework’s defined metrics and in multiple scenarios. We find that the latter provides substantial advantages for certain classes of inertial sensors. Our framework allows to consider a wide range of problems related to the quantification of navigation system performances, such as the robustness of integrated navigation systems (such as INS/GNSS) with respect to outliers or other modeling imperfections. While real world experiments are essential to assess to performance of new methods, they tend to be costly and are typically unable to lead to a sufficient number of replicates to provide suitable estimates of, for example, the correctness of the estimated uncertainty. Therefore, our method can contribute in bridging the gap between these experiments and pure statistical consideration as usually found in the stochastic calibration literature.

Markovian approach to evaluate circularity in supply chain of non ferrous metal industry

The development of a Circular Economy is essential to the attainment of sustainable development goals. The adoption of circular strategies is either at system level or product level. However, the exploration of circularity of material flow in case of developing economies is still limited in the existing literature. Therefore, the study aims to identify the circularity potential of non-ferrous materials like Aluminium extracted from the products. A case of the Indian Aluminium industry is considered for the study. In proposed study, the Markov Chain method is used as a stochastic modeling technique to explore the degree of circularity in the material flow analysis of aluminium through its various lifecycle stages. The novelty of this paper is two-fold: (1) it gives an insight about the material movement in the circular supply chain depending upon its current state and the time during which it remains in the respective state, and (2) it also gives a brief idea about the circularity of metal flow at different stages such as recycling of Aluminium Circular Supply Chain. From the results of Markov Chain model as applied to Indian Aluminium industry, it is observed that irrespective of the material being in any of the state, most likely it goes to the landfill after completing its average useful life. Further, findings of the study reveal that very low percentage of raw material goes to the recycling stage. Lastly, the reducing trend in the circularity from production to consumption reflects lack of circular initiatives adopted in the downstream sectors of material flow. Markov chain method not only helps the decision maker to identify the preferred strategy but also provides important information about the material movement while adopting a particular circular strategy. This study guide the future studies to effectively measure circularity under all circumstances and across all sectors.

Stochastic Guarantees for Adaptive Energy Harvesting Systems

Energy harvesting is increasingly used as a long-term energy supply for the Internet of Things, wireless sensor networks, and cyber-physical systems. However, the challenge of mitigating the variability of energy harvesting sources needs to be addressed before ubiquitous adoption can happen. Otherwise, an unreliable operation of devices with frequent shutdowns during times of energy scarcity would be encountered. One finds probabilistic performance metrics helpful in designing power management solutions for the long-term operation of energy harvesting nodes. These metrics include the probability of battery depletion, expected energy consumption, expected battery level, and similar. This article proposes a stochastic modeling technique and corresponding analysis which can provide such metrics. Our advanced analysis is based on Markov chains. By modeling harvested energy with random variables, new and existing energy management policies are analyzed and compared. We propose an adaptive energy management strategy inspired by mixed-criticality systems. In the proposed strategy, the system can degrade or drop less essential tasks in real time to ensure a graceful degradation of service in adverse harvesting conditions. We compare the proposed energy management approach to several existing alternatives. To this end, we conduct extensive simulations for indoor and outdoor environments, where our strategy matches or outperforms the state of the art. Initial results also validate the high precision of our stochastic model and analysis in comparison to simulations using real-world data.

A Tractable, Transferable, and Empirically Consistent Fibrous Biomaterial Model

Stochastic modeling is a useful approach for modeling fibrous materials that attempts to recreate fibrous materials’ structure using statistical data. However, several issues remain to be resolved in the stochastic modeling of fibrous materials—for example, estimating 3D fiber orientation distributions from 2D data, achieving the desired fiber tortuosity distributions, and dealing with fiber–fiber penetration. This work proposes innovative methods to (1) create a mapping from 2D fiber orientation data to 3D fiber orientation probability distributions, and vice versa; and (2) provide a means to select parameters de novo for random walks employing the popularized von Mises–Fisher distribution given that the desired tortuosity of the path is known. The proposed methods are incorporated alongside previously developed stochastic modeling techniques to simulate fiber network structures. First, fiber orientation distributions vary significantly depending on how a fibrous material is formed, and projection distortion affects the measurement of fiber orientation distributions when reported as 2D data such as histograms or polar plots. Relationships are developed to estimate 3D fiber orientation distributions from 2D data, accounting for projection distortion and the variety of orientation distributions observed in fibrous materials. We show that without correcting for projection distortion, fiber orientation distribution parameters could have errors of up to 100%. Second, in stochastic modeling, fiber tortuosity is usually treated with random walks, but no relationship is available for choosing random walk inputs to generate a desired fiber tortuosity. Relationships are also developed to relate the input parameters of von Mises–Fisher random walks to the expected tortuosity of the generated path—a necessary link to modeling fiber tortuosity distributions tractably and with empirical consistency. Using the developed relationships, we show that modeling of tortuous fibers from a distribution could be sped up by ~1200-fold and the uncertainty of selecting appropriate parameters could be eliminated. Third, randomly placing fibers in a simulation domain inevitably results in fiber–fiber penetration, and correcting this issue requires changes to the simulated fibrous material structure through non-penetration conditions. No thorough remedy can be offered here, but we statistically quantify the effects of enforcing non-penetration conditions on the fiber shape and orientation changes as well as the overall fibrous material model. This work offers tractable and transferable methods for treating fiber orientation and tortuosity that allow for empirical consistency in the stochastic modeling of fibrous materials.

Optimal control theory of a novel stochastic human norovirus model and vaccine development

Norovirus is a contagious disease that causes diarrhea and vomiting and has a significant impact on humanity in terms of medical costs, deaths and mortalities. In this research work, the stochastic modeling techniques are utilized and a novel human norovirus model is investigated keeping in view the contamination of food and water with vaccination effects. It is proved that the model has a unique global solution and by using Lyapunov function theory, sufficient conditions are derived under which the proposed model has a unique ergodic stationary distribution for [Formula: see text]. It is observed that the disease will extinct out of the population whenever [Formula: see text]. To demonstrate the analytical results, two independent examples are depicted graphically by using standard numerical algorithm. To reduce the spread of the virus, we employed certain control measures and an optimal control problem is presented. To further validate the obtained analytical results, additional graphical solutions were generated. This study might provide a robust theoretical framework for a global understanding of chronic communicable illnesses. Our method also aims to provide a method for producing Lyapunov functions, which can be used to explore the stationary distribution of disease models having nonlinear stochastic perturbations.