Representative Mathematical Models Research Articles

Modeling of cell cultivation for monoclonal antibody production processes considering lactate metabolic shifts.

Demand for monoclonal antibodies (mAbs) is rapidly increasing. To achieve higher productivity, there have been improvements to cell lines, operating modes, media, and cultivation conditions. Representative mathematical models are needed to narrow down the growing number of process alternatives. Previous studies have proposed mechanistic models to depict cell metabolic shifts (e.g., lactate production to consumption). However, the impacts of variations of some operating conditions have not yet been fully incorporated in such models. This paper offers a new mechanistic model considering variations in dissolved oxygen and glutamine depletion on cell metabolism applied to a novel Chinese hamster ovary (CHO) cell line. Expressions for the specific rates of lactate production, glutamine consumption, and mAb production were formulated for stirred and shaken-tank reactors. A deeper understanding of lactate metabolic shifts was obtained under different combinations of experimental conditions. Lactate consumption was more pronounced in conditions with higher DO and low glutamine concentrations. The model offers mechanistic insights that are useful for designing advanced operation strategies. It can be used in design space generation and process optimization for better productivity and product quality.

New Hydrophilic Matrix Tablets for the Controlled Released of Chlorzoxazone.

The modified release of active substances such as chlorzoxazone from matrix tablets, based on Kollidon®SR and chitosan, depends both on the drug solubility in the dissolution medium and on the matrix composition. The aim of this study is to obtain some new oral matrix tablet formulations, based on Kollidon®SR and chitosan, in order to optimize the low-dose oral bioavailability of chlorzoxazone, a non-steroidal anti-inflammatory drug of class II Biopharmaceutical Classification System. Nine types of chlorzoxazone matrix tablets were obtained using the direct compression method by varying the components ratio as 1:1, 1:2, and 1:3 chlorzoxazone/excipients, 20-40 w/w % Kollidon®SR, 3-7 w/w % chitosan while the auxiliary substances: Aerosil® 1 w/w %, magnesium stearate 0.5 w/w % and Avicel® up to 100 w/w % were kept in constant concentrations. Pharmaco-technical characterization of the tablets included the analysis of flowability and compressibility properties (flow time, friction coefficient, angle of repose, Hausner ratio, and Carr index), and pharmaco-chemical characteristics (such as mass and dose uniformity, thickness, diameter, mechanical strength, friability, softening degree, and in vitro release profiles). Based on the obtained results, only three matrix tablet formulations (F1b, F2b, and F3b, containing 30 w/w % KOL and 5 w/w % CHT, were selected and further tested. These formulations were studied in detail by Fourier-transform infrared spectrometry, X-ray diffraction, thermogravimetry, and differential scanning calorimetry. The three formulations were comparatively studied regarding the release kinetics of active substances using in vitro release testing. The results were analyzed by fitting into four representative mathematical models for the modified-release oral formulations. In vitro kinetic study revealed a complex mechanism of release occurring in two steps of drug release, the first step (0-2 h) and the second (2-36 h). Two factors were calculated to assess the release profile of chlorzoxazone: f1-the similarity factor, and f2-the factor difference. The results have shown that both Kollidon®SR and chitosan may be used as matrix-forming agents when combined with chlorzoxazone. The three formulations showed optima pharmaco-technical properties and in vitro kinetic behavior; therefore, they have tremendous potential to be used in oral pharmaceutical products for the controlled delivery of chlorzoxazone. In vitro dissolution tests revealed a faster drug release for the F2b sample.

On Combining Shape Memory Alloy Actuators and Pneumatic Actuators for Performance Enhancement in Soft Robotics

Through soft robotics, flexible structures confer an elevated degree of protection and safety in usage, as well as precision and reliability. Using theoretical models while combining different types of soft components opens a wide variety of possibilities for the development of new and better alternatives to rigid robots. Modeling and controlling soft robotic structures is still a challenge and is presented in different ways by the scientific community. The present scientific work aims to combine two of the most popular types of soft actuators, specifically shape memory alloy and pneumatic actuators. The purpose is to observe the interaction between individual entities and the resulting combined dynamics, highlighting the distinctive effects and influences observed in the combined system. An evaluation is conducted from a numerical simulation perspective in the MATLAB environment using representative mathematical models. The tests prove that a structure combining these particular actuators benefits from the advantages of both components and even compensates for individual downsides.

Optimization of synthesis parameters of PUF/ENB microcapsules for self‐healing applications using factorial design methodology

AbstractThis study introduces a systematic experimental approach aimed at enhancing the production process of poly(urea‐formaldehyde) (PUF) microcapsules filled with 5‐ethylidene‐2‐norbonene (ENB) using in situ emulsion polymerization. Essential parameters were identified through a prior Plackett Burman (PB) design, leading to the implementation of a 24‐1 fractional factorial design. The key parameters selected encompassed stirring speed, poly(ethylene‐alt‐maleic anhydride) (EMA) emulsifier content, pH of the reaction, and the quantity of 1‐octanol. Optimal conditions for polymeric microcapsule synthesis were determined using a statistical analysis of the complete factorial design, facilitating the development of representative mathematical models for the process. A comprehensive evaluation of response variables including microcapsule diameter, yield, encapsulated content, stability, and thermal degradation was conducted. Utilizing response surface analysis (RSM), it was determined that the PUF/ENB(2C) condition (stirring at 700 rpm, a reaction pH of 3.0, and EMA content of 0.425 g) resides within the optimized synthesis region, producing microcapsules exhibiting favorable morphological characteristics, yield of 52% and encapsulated content of 80%.

Airline scheduling optimization: literature review and a discussion of modelling methodologies

Abstract The rapid development of civil aviation in recent decades has not only led to increasing competition among airlines, but also to the rise of irregularities, with challenges concerning the improvement of regulations and schedules under the maximization of profitability. Consequently, the airline scheduling optimization problem has received significant research interest as the foundation for an efficient deployment of airline resources and meeting market demand under complex operational requirements. In this paper, we dissect fundamental airline scheduling problems by reviewing thirteen representative mathematical models for schedule design, fleet assignment, aircraft routing, crew scheduling subproblems and their potential for integration. In contrast to existing review studies on airline scheduling problems, our main contribution lies in the introduction of state-of-the-art mathematical models with a specific focus on integration and robustness. In addition, we highlight a set of promising, yet challenging, directions for future research in this domain.

The Drone Scheduling Problem: A Systematic State-of-the-Art Review

Drones are receiving popularity with time due to their advanced mobility. Although they were initially deployed for military purposes, they now have a wide array of applications in various public and private sectors. Further deployment of drones can promote the global economic recovery from the COVID-19 pandemic. Even though drones offer a number of advantages, they have limited flying time and weight carrying capacity. Effective drone schedules may assist with overcoming such limitations. Drone scheduling is associated with optimization of drone flight paths and may include other features, such as determination of arrival time at each node, utilization of drones, battery capacity considerations, and battery recharging considerations. A number of studies on drone scheduling have been published over the past years. However, there is a lack of a systematic literature survey that provides a holistic overview of the drone scheduling problem, existing tendencies, main research limitations, and future research needs. Therefore, this study conducts an extensive survey of the scientific literature that assessed drone scheduling. The collected studies are grouped into different categories, including general drone scheduling, drone scheduling for delivery of goods, drone scheduling for monitoring, and drone scheduling with recharge considerations. A detailed review of the collected studies is presented for each of the categories. Representative mathematical models are provided for each category of studies, accompanied by a summary of findings, existing gaps in the state-of-the-art, and future research needs. The outcomes of this research are expected to assist the relevant stakeholders with an effective drone schedule design.

Data-driven simultaneous identification of the 6DOF dynamic model and wave load for a ship in waves

In marine operations, the performance of model-based automatic control design and decision support systems highly relies on the accuracy of the representative mathematical models. Model fidelity can be crucial for safe voyages and offshore operations. This paper proposes a data-driven parametric model identification of a ship with 6 degrees of freedom (6DOF) exposed to waves using sparse regression according to the vessel motion measurements. The features of the complex ship dynamics are extracted and expressed as a linear combination of several functions. Thruster inputs and environmental loads are considered. The hydrodynamic coefficients and wave-induced loads are simultaneously estimated. Unlike earlier studies using a limited number of unknown functions, a library of abundant candidate functions is applied to fully consider the coupling effects among all DOFs. The benefit of the proposed method is that it does not require the exact construction of the library functions. Based on the estimated model, short-term motion prediction is achievable. The algorithm is verified through experiments. The method can be extended to other types of floating structures.

Modeling and simulation of magnetorheological dampers for the reduction of the seismic response of structures using simulink

The control devices can be used to dissipate the energy of structures subjected to dynamic loads in order to reduce structural damage and prevent the failure of them. The semiactive control devices that have received great attention in recent years are magnetorheological (MR) fluid dampers due to their mechanical simplicity, high dynamic range, large temperature operating range and low power requirements. In the present research work, Matlab and Simulink are used as computational tools for the modeling and simulation of structural control systems with magnetorheological dampers (MRDs). To begin with, the modeling is carried out through simulink block diagrams of the governing differential equations of representative mathematical models of MRDs. Next, a series of simulations is performed in order to replicate experimental results and to be able to validate the modeling step. Finally, the MRDs are integrated together with a semiactive control algorithm and an idealized ten-degrees-of-freedom structure. The main expected outcome is the reduction of the seismic response (response histories, drifts, shear forces and overturning moments).

Proposing a novel double sigmoidal model to fit the master curve for various polymer-modified asphalt

ABSTRACT Master curve technique is frequently used to characterize the linear viscoelasticity of polymer modified asphalt (PMA), however, there is no widely accepted master curve for PMA. This study aims to propose a novel double sigmoidal model that can be used universally for all asphalts, especially highly modified PMAs. To do so, one plain asphalt and six representative PMAs are examined. Extended temperature sweep tests (−40°C to 140°C) are conducted to grasp the whole picture of the master curve. Three representative mathematical models (CAM, sigmoidal, double sigmoidal) are selected and compared in terms of fitting in both modulus and phase angle. The results suggest that double sigmoidal model suits all types of asphalts for all testing temperature ranges, and it features the ability to model the rubbery state and rubbery-viscous transition of highly modified PMA (RMSE < 0.02). A phase angle expression of the double sigmoidal model is also developed, which shows great potential in characterizing the strength of polymer network within the PMA. Also, it avoids the impact from the partial break of the time-temperature superposition principle (TTSP) and reveals the true shape of the phase angle master curve. Finally, master curve models are recommended based on different testing temperature ranges.

Uncertainties in Liner Shipping and Ship Schedule Recovery: A State-of-the-Art Review

Each shipping line is expected to establish a reliable operating model, and the design of ship schedules is a key operational consideration. Long-term profits for shipping lines can be expected from a well-designed ship schedule. In today’s liner service design, managing the time factor is critical. Shipping schedules are prone to different unexpected disruptions. Such disruptions would necessitate a near-real-time analysis of port capacity and re-design of the original ship schedule to offset the negative externalities. Ship schedule recovery strategies should be implemented to mitigate the effects caused by disruptions at ports or at sea, which may include, but are not limited to, ship sailing speed adjustment, handling rate adjustment at ports, port skipping, and port skipping with container diversion. A proper selection of ship schedule recovery strategies is expected to minimize deviations from the original ship schedule and reduce delays in the delivery of cargoes to the destination ports. This article offers a thorough review of the current liner shipping research primarily focusing on two major themes: (1) uncertainties in liner shipping operations; and (2) ship schedule recovery in response to disruptive events. On the basis of a detailed review of the available literature, the obtained results are carefully investigated, and limitations in the current state-of-the-art are determined for every group of studies. Furthermore, representative mathematical models are provided that could be further used in future research efforts dealing with uncertainties in liner shipping and ship schedule recovery. Last but not least, a few prospective research avenues are suggested for further investigation.

Copper Mineral Leaching Mathematical Models-A Review.

Mineral leaching is the key unit operation in metallurgical processes and corresponds to the dissolution of metals. The study of leaching is carried out in many areas, such as geology, agriculture and metallurgy. This paper provides an introduction to the theoretical background regarding the mathematical modelling of the leaching process of copper minerals, establishing an overall picture of the scientific literature on technological developments and the generation of representative mathematical and theoretical models, and indicating the challenges and potential contributions of comprehensive models representing the dynamics of copper mineral leaching.

Selection of the modeling resolution of infrastructure

AbstractAccurate risk analysis requires representative mathematical models of infrastructure. One of the main challenges in developing mathematical models of infrastructure is selecting the modeling resolution from multiple candidates for the required analyses, each candidate having different computational cost, accuracy, and possibly ability to provide information. The goal of selecting the model resolution is to allocate computational resources to the model that best delivers the desired information with the desired accuracy level. This paper proposes a mathematical formulation to select the appropriate resolution for the modeling of infrastructure. We formulate the model selection as an iterative process until a tradeoff is achieved among accuracy, simplicity, and computational efficiency. To select the appropriate level of resolution, we propose novel metrics that measure the level of agreement between estimates of the quantities of interest computed using different levels of resolution. Specifically, we propose global metrics of accuracy that inform if a model is sufficiently detailed or oversimplified. Likewise, we introduce local metrics of accuracy to inform which parts of the model (e.g., spatial portions of the infrastructure model) need refinements. We illustrate the proposed mathematical formulation by selecting the level of resolution of the water infrastructure of Seaside, Oregon, for the purpose of assessing its functionality after a seismic hazard.

A Framework for Archive Demand Management Strategies: A Pilot Study on Water Use in a Low-Income Brazilian Area

This study presents a pilot study in suburban households in Salvador, Brazil, inserted in the context of a framework developed to aid water demand management strategies. The framework aims to understand the barrier of subjectivity while identifying consumption habit patterns in households. Six key sets of components create the framework architecture: (1) characterization of the area based on: context, climate, population/area, population growth rate, and water management challenges; (2) a survey to obtain socio-demographic and physical property data of the sample; (3) smart metering and data processing systems to monitor sample water end use; (4) determining daily consumption patterns; (5) analyzing qualitative data through theoretical consumption models to identify relevant variables for the next step; and (6) construction of representative mathematical models of consumption for each daily practice (this item was not included on pilot). It provides a starting point to understand how water demand management strategies can be supported at the user and decision-making level. As a result, improvements to the interview guides used in the pilot were suggested. Furthermore, customized measures to promote rational water consumption were identified in the study area, and policies could be proposed.

Identification of multiple local nonlinear attachments using a single measurement case

This research focuses on the construction of representative mathematical models for the dynamics of multiple local nonlinear attachments installed on the same primary structure. Specifically, the applicability of the recently developed characteristic nonlinear system identification (CNSI) to multiple attachments and attachments tuned to modes higher than the first linear mode of the primary structure is investigated. The CNSI procedure is a data-driven approach that produces a mathematical model for the dynamics of local nonlinear attachments directly from experimental measurements with the only knowledge of the mass of the attachment and the general frequency content required. The applicability of the CNSI method for multiple attachments is demonstrated using a two-story tower with one local nonlinear attachment installed on each floor in two configurations. In the first configuration, both attachments are tuned to interact with the first mode of the tower. In the second configuration, the linear stiffness of the attachment installed on the first floor is increased, such that it interacts with the second mode instead of the first. The resulting models are numerically integrated, and the resulting displacements are directly compared with the experimental measurements. This comparison provides validation of the success and strength of the CNSI method for identifying multiple nonlinear attachments using a single measurement case. The method is particularly suitable for transient response data, and it is unlikely that the method would work with harmonic and random excitation responses. The method also might not be ideal for systems having inflexible impacts or asymmetric restoring forces.

A Survey on Canonical Correlation Analysis

In recent years, the advances in data collection and statistical analysis promotes canonical correlation analysis (CCA) available for more advanced research. CCA is the main technique for two-set data dimensionality reduction such that the correlation between the pairwise variables in the common subspace is mutually maximized. Over 80-years of developments, a number of CCA models have been proposed according to different machine learning mechanisms. However, the field lacks an insightful review for the state-of-art developments. This survey targets to provide a well-organized overview for CCA and its extensions. Specifically, we first review the CCA theory from the perspective of both model formation and model optimization. The association between two popular solution methods, i.e., eigen value decomposition (EVD) and singular value decomposition (SVD), are discussed. Following that, we present a taxonomy of current progresses and classify them into seven groups: 1) multi-view CCA, 2) probabilistic CCA, 3) deep CCA, 4) kernel CCA, 5) discriminative CCA, 6) sparse CCA and 7) locality preserving CCA. For each group, we demonstrate two or three representative mathematical models, identifying their strengths and limitations. We summarize the representative applications and numerical results of these seven groups in real-world practices, collecting the data sets and open-sources for implementation. In the end, we provide several promising future research directions that can improve the current state of the art.

Simple analytical models for restrained steel columns in fire

In structural engineering, two distinct types of computational strategies can be used to analyse a frame under the action of forces. The first type applies to any general structure and incorporates all involved complexities in the mathematical model. It aims to represent as accurately as possible all involved phenomena and leads usually to very complex numerical models, such as the Finite Elements ones. In contradistinction to this, the alternative strategies adopt simple but representative mathematical models that focus on a specific phenomenon. Despite their limited range of application, simple mathematical models enable an easier analysis of the key phenomena without forfeiting accuracy. They also provide a good depiction of the true physical response. Within this latter context, the present work presents two simplified structural models for the analysis of restrained elasto-plastic steel columns under fire conditions: i) an adapted Shanley model and ii) a two rigid rods frame joined by a plastic hinge. Only uniform heating is considered, as reference, and all nonlinear properties are taken into account, namely the degradation of the steel’s properties with heating, the nonlinear constitutive behaviour and the instability effects arising from the restraining of the thermal elogation. These two models enable the computation of the critical temperature, which defines the column’s strength in case of fire, with minimum effort and within an acceptable accuracy.

An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

The dynamic analysis of systems has several applications in the project or monitoring and controlling machines and equipments. In particular, the analysis of nonlinear systems has academic and industrial appeal for owning many particularities such as structural integrity, models updating, stability and real-time predictability. Those particularities complicate the study of these models. However, the development of more representative mathematical models requires normally costly computations. By considering the uncertainties associated with the fabrication process (geometrical dimensions, physical and material properties), as well as those related to the operational conditions (boundary conditions, external forces, etc.), it complicates further the analysis of those nonlinear systems. Thus, this paper proposes a methodology to analyze nonlinear systems subjected to uncertainties using the stochastic finite element method. In view of the high computational cost needed to construct the confidence region predicted with the stochastic nonlinear computational model, it is proposed herein a new model reduction method based on the construction of an adaptive iterative enriched basis to deal with the stochastic nonlinear system addressed herein composed by a thin rectangular plate used as an application. The results demonstrate clearly the efficiency and accuracy of the proposed method as an efficient tool to approximate the nonlinear responses of more complex nonlinear systems subjected to uncertainties. Also, it demonstrates the relevance of taking into account the uncertainties in the modeling of nonlinear systems to consider more realistic situations.

Chromium(VI) Removal by Polyvinyl Chloride (PVC)/Aliquat-336 Polymeric Inclusion Membranes in a Multiframe Flat Sheet Membrane Module

A new multiframe flat sheet membrane contactor module containing several flat membranes was designed and implemented. Each frame contains a chamber (central hole) in which the feed and the receiving phases are put in contact with polyvinyl chloride (PVC)/Aliquat-336 polymeric flat sheet membranes for Cr(VI) removal from aqueous solutions (feed phase). To evaluate the efficiency of the system, the experimental design methodology was used to analyze the effect of temperature (T, °C), PVC/Aliquat-336 ratio, and Cr (VI) concentration in the feed phase and the concentration of sodium chloride (NaOH-NaCl) in the receiving phase. Two representative mathematical models of the two responses (extraction and back-extraction) were respectively obtained. A good correlation between the experimental results and those predicted (RS2 = 97.77 and RR2 = 97.87) was achieved, allowing the optimization of the different factors selected for each response, separately. The proposed system showed a good separation performance, leading to Cr(VI) extractions up to 93% when working at the optimized operating conditions.

Numerical analysis of hemivariational inequalities in contact mechanics

Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.

Radiotracer investigation and modeling of an activated sludge system in a pulp and paper industry

A radiotracer investigation was carried out in an activated sludge process (ASP) system of an effluent treatment plant in a pulp and paper industry. The system consists of an aeration tank and a secondary clarifier connected in series. The primary objective of the investigation was to measure mean hydraulic retention times (MHRTs) of wastewater and investigate the hydraulic performance of the ASP. Residence time distributions (RTD) of the wastewater were measured in an aeration tank and a secondary clarifier of the system using Iodine-131 as a radiotracer. The measured RTD data was treated and MHRTs were estimated. No bypassing was found to exist in the aeration tank and the secondary clarifier. However, the dead volume in the aeration tank and the secondary clarifier was found and estimated to be 2.34% and 4.6%, respectively. The treated curves were further simulated using suitable hydraulically representative mathematical models and detailed flow patterns in the aeration tank and the secondary clarifier were deciphered.