Analysis Of Mathematical Model Research Articles

Mathematical modeling of coating time in dry particulate coating using mild vibration field with bead media described by DEM simulation

• A simple stochastic saturation model for dry coating process was developed. • Model introduces assumption one collision causes one particle to adhere on the core. • Unfixed coating particle on the surface of core decrease over time on the model. • Change in the coating ratio is determined by the number of collisions and particles. To theoretically understand the previously reported dry particulate coating process using a mild vibration field with a bead media, a mathematical analysis model of the dry coating system was developed. In this coating process, an ordered mixture with coarse host particles (drug-loaded ion exchange resin, diameter approximately 100 µm) and fine guest particles (acrylic polymer particle, primary particle size of approximately 100 nm) is formed using a vibrating a vessel. Second, the guest particles on the host particulate surface are firmly fixed using the collision of coated particles zirconia beads (diameter 1.5 mm). Our model assumes that the unfixed guest particles are fixed by particle-to-particle collisions ( C c ) provided by the apparatus, thereby increasing the coating ratio. C c was estimated using the discrete element method and some experimental results. The model includes parameters such as the number of C c , host particles and unfixed guest particles. The coating time simulated by the established model equation in this study fits well with the experimental results of the dry process. It depends on the ratio of the number of collisions contributing to the increased coating ratio to the number of unfixed guest particles on the surface of host particles.

Experimental and Modeling Study on Cr(VI) Migration from Slag into Soil and Groundwater

The transport and prediction of hexavalent chromium (Cr(VI)) contamination in “slag–soil–groundwater” is one with many uncertainties. Based on the column experiments, a migration model for Cr(VI) in the slag–soil–groundwater system was investigated. The hydraulic conductivity (Kt), distribution coefficient (Kd), retardation factor (Rd), and other hydraulic parameters were estimated in a laboratory. Combining these hydraulic parameters with available geological and hydrogeological data for the study area, the groundwater flow and Cr(VI) migration model were developed for assessing groundwater contamination. Subsequently, a Cr(VI) migration model was developed to simulate the transport of Cr(VI) in the slag–soil–groundwater system and predict the effect of three different control programs for groundwater contamination. The results showed that the differences in the measured and predicted groundwater head values were all less than 3 m. The maximum and minimum differences in Cr(VI) between the measured and simulated values were 1.158 and 0.001 mg/L, respectively. Moreover, the harmless treatment of Cr(VI) slag considerably improved the quality of groundwater in the surrounding areas. The results of this study provided a reliable mathematical model for transport process analysis and prediction of Cr(VI) contamination in a slag–soil–groundwater system.

Mathematical modeling of the kinetics of a single intake of ethanol

The aim of the study is to construct a kinetic equation of zero-order ethanol elimination with first-order absorption, taking into account the presystemic metabolism of ethanol, with the possibility of determining the errors in estimating the parameters of the model, as well as the implementation of the model in the format of a computer program. Analytical mathematical modeling of the kinetics of a single oral intake of ethanol has been performed. A mathematical model of the kinetics of a single intake of ethanol with its zero-order elimination, absorption and first-order presystemic metabolism has been developed. A method is proposed for estimating the limiting absolute errors of the kinetic parameters of the constructed model based on the summation of the partial contributions of the initial physical quantities. The complex of the developed computational procedures is implemented in the format of the «Alcohol Calculator V 1.0» computer program. The conclusion is made about the expediency of using the developed information and computing technology in the forensic medical expert assessment of acute alcohol intoxication.

Mathematical modeling of the kinetics of a single intake of ethanol

The aim of the study is to construct a kinetic equation of zero-order ethanol elimination with first-order absorption, taking into account the presystemic metabolism of ethanol, with the possibility of determining the errors in estimating the parameters of the model, as well as the implementation of the model in the format of a computer program. Analytical mathematical modeling of the kinetics of a single oral intake of ethanol has been performed. A mathematical model of the kinetics of a single intake of ethanol with its zero-order elimination, absorption and first-order presystemic metabolism has been developed. A method is proposed for estimating the limiting absolute errors of the kinetic parameters of the constructed model based on the summation of the partial contributions of the initial physical quantities. The complex of the developed computational procedures is implemented in the format of the «Alcohol Calculator V 1.0» computer program. The conclusion is made about the expediency of using the developed information and computing technology in the forensic medical expert assessment of acute alcohol intoxication.

Analytical Solutions to Fundamental Questions for Lossy Mode Resonance

AbstractLossy mode resonance (LMR) is an optical resonance phenomenon developed in the past decade, which has been researched for sensors and filters due to its high sensitivity, low loss, and broad tunable range. As a novel technology, if an analytical mathematical model for some fundamental questions like how to design the resonance wavelength, surrounding sensitivity, resonance width, and resonance depth, it will be guiding significance to its development. Herein, this paper develops a generalized Fabry–Perot resonance theory for LMR, where the oblique incidence, cavity loss, and dispersion of substrate and cavity are comprehensively considered, and the consistency of this model and a more rigorous guided wave optics model have been verified. Then, analytical mathematical models are established and analyzed, and the designing criterion for LMR‐based optical devices is proposed. After intensive reviewing the work of predecessors, the previous experimental results are consistent with the prediction of this model, and this model can also provide some new ideas that have not been researched yet. As an assistant to wave optics theory, this paper provides a second perspective to understand LMR phenomenon, and it is hoped the analytical solutions for LMR can be a guide for designing optical devices.

Balancing Infectious Disease Control and Radiotherapy Risk Management Using a Novel Analytic Approach

<h3>Purpose/Objective(s)</h3> To develop an analytic risk management method that uses mathematical models in Failure Modes and Effects Analysis (FMEA) to design mitigation efforts to control pandemic infection, while ensuring safe delivery of radiotherapy. <h3>Materials/Methods</h3> A two-stage FMEA approach is proposed to modify radiotherapy workflow during a pandemic. In stage 1, an Infection Control FMEA (IC-FMEA) is conducted, where risks are evaluated based on environmental parameters, clinical interactions, and modeling of the pandemic infection risk. Occupancy` Risk Index (ORI) is defined as a metric of infection risk probability in each room, based on the degree of occupancy during clinical operations. ORI, in combination with ventilation rate per person (R_p), is used to provide a broad infection risk assessment of workspaces. For detailed IC-FMEA of clinical processes, Infection containment failure mode (ICFM) is defined to be any instance of disease transmission within the clinic. Infection risk priority number (IRPN) has been formulated as a function of time, distance, and degree of protective measures. Infection control measures are then systematically integrated into the workflow. In stage 2, a conventional radiotherapy FMEA (RT-FMEA) can be performed on the adjusted workflow. A number of different clinical processes within radiotherapy workflow have been evaluated with this approach. <h3>Results</h3> The COVID-19 pandemic was used to illustrate stage 1 IC-FMEA. ORI and R_p values were calculated for various workspaces within a radiotherapy clinic. A deep inspiration breath hold (DIBH) CT simulation was used as an example to demonstrate detailed IC-FMEA with ICFM identification and IRPN evaluation. A total of 90 ICFMs were identified in the DIBH process. For minimal protective measures the IRPN values ranged from 2 – 1200, while for increasing degrees of infection control the values decreased to 2-530 and 1-189 corresponding to moderate and enhanced measures respectively. <h3>Conclusion</h3> The framework developed in this work provides tools for radiotherapy clinics to analytically assess risks and adjust workflows during a pandemic.

Study on the Performance of a Solar Heating System with Seasonal and Cascade Thermal-Energy Storage

Seasonal solar thermal-energy storage systems used for space heating applications is a promising technology to reduce greenhouse gas emissions. A novel solar heating system with seasonal and cascade thermal-energy storage based on zeolite water is proposed in this study. The system’s efficiency is improved through cascade storage and the release of solar energy. The energy storage density is improved through the deep coupling of daily energy storage and cross-seasonal energy storage. A mathematical model of the system-performance analysis is established. The system performances in the non-heating and heating seasons and throughout the year are analyzed by considering the Chifeng City of China as an application case. The results indicate that the average collection efficiency of the proposed system is 2.88% higher in the non-heating season and 7.4% higher in the heating season than that of the reference system. Furthermore, the utilization efficiency of the proposed system is 37.16%, which is 3.26% higher than that of the reference system. Further, the proposed system has a supply heat of 2135 GJ in the heating season, which is 9.66% higher than the reference system. This study provides a solution for the highly efficient solar energy utilization for large-scale space-heating applications.

Connecting the dots: A practical evaluation of web-tools for describing protein dynamics as networks.

Protein Structure Networks (PSNs) are a well-known mathematical model for estimation and analysis of the three-dimensional protein structure. Investigating the topological architecture of PSNs may help identify the crucial amino acid residues for protein stability and protein-protein interactions, as well as deduce any possible mutational effects. But because proteins go through conformational changes to give rise to essential biological functions, this has to be done dynamically over time. The most effective method to describe protein dynamics is molecular dynamics simulation, with the most popular software programs for manipulating simulations to infer interaction networks being RING, MD-TASK, and NAPS. Here, we compare the computational approaches used by these three tools-all of which are accessible as web servers-to understand the pathogenicity of missense mutations and talk about their potential applications as well as their advantages and disadvantages.

Wrapper Functions for Integrating Mathematical Models into Digital Twin Event Processing.

Analog sensors often require complex mathematical models for data analysis. Digital twins (DTs) provide platforms to display sensor data in real time but still lack generic solutions regarding how mathematical models and algorithms can be integrated. Based on previous tests for monitoring and predicting banana fruit quality along the cool chain, we demonstrate how a system of multiple models can be converted into a DT. Our new approach provides a set of generic “wrapper functions”, which largely simplify model integration. The wrappers connect the in- and outputs of models to the streaming platform and, thus, require only minor changes to the model software. Different scenarios for model linking structures are considered, including simultaneous processing of multiple models, sequential processing of life-cycle-specific models, and predictive models, based on data from the current and previous life cycles. The wrapper functions can be easily adapted to host models or microservices from various applications fields, to predict the future system behavior and to test what-if scenarios.

EFFECTIVENESS ASSESSMENT OF USING ENTERPRISE`S PRODUCTION AREAS AND ITS IMPACT ON PROFIT CHANGES

The article considers the method of modeling and factorial analysis of the company's profit indicator. It is proposed to use deterministic mathematical profit models in the factorial analysis of this indicator, which contain a number of different factors that characterize the size, structure and efficiency of the use of the land area occupied by the enterprise. When the building of deterministic factorial system happens, it is recommended to calculate the quantitative influence on the overall change of the investigated profit indicator such important factors as the total area occupied by the analyzed enterprise, the production area on which the production process is directly carried out, the area directly occupied by the production equipment, employment rates total and production area, production output and the amount of profit per unit of the corresponding area, the level of production profitability. In order to assess the quantitative impact of these factors on the overall change of the studied profit indicator, it is suggested to carry out its step-by-step factor analysis, that is, to sequentially calculate the influence of two factors first, then three, etc. This makes it possible at each stage of the factor analysis to quickly determine the impact on the change in profit of only those factors that are the most relevant for the given enterprise at this moment in time. Factor analysis of profit is proposed to be carried out with the help of an index modification of the method of chain substitutions, which involves the use of indices of factor indicators, and not their absolute values, in analytical calculations. The relative influence of the specified factors on the overall change in profit is calculated by the ratio of the obtained absolute influence of each factor to its absolute value in the base period. The given method of modeling and factor analysis of profit makes it possible to decompose this indicator into a number of primary constituent parts, to give an analytical assessment of the impact of the efficiency of the use of production areas of the enterprise on its change, to identify the patterns of such influence, to use the information obtained to substantiate the relevant management decisions regarding the development of development tactics and strategies enterprises for the future period. Keywords: method, production area, factor analysis, method of chain substitution, profit.

A review on use of computational biology in testing of skeletal muscle function in COPD patients

Computer biology and bioinformatics are interdisciplinary fields that develop and apply computational methods to analyse large amounts of biological data, such as genetic sequences, cell populations, or protein samples, in order to make new predictions or find novel biology. Analytical approaches, mathematical modelling, and simulation are among the computational methods employed.Chronic Obstructive Pulmonary Disease (COPD) is a lung inflammatory disease that causes persistent airflow restriction. These individuals frequently have extensive systemic consequences, such as skeletal muscle dysfunction, which severely restrict their life expectancy. Despite extensive research, the molecular basis of muscle deterioration in COPD remains a matter of contention. We used a network biology approach to investigate the link between the molecular and physiological responses of muscles to training and systemic inflammatory mediators in this study. Failure to coordinately activate expression of various tissue remodelling and bioenergetics pathways is a distinctive feature of COPD diseased muscles, according to our model. Our findings also point to a relationship between this phenomena and aberrant expression of a number of histone modifiers, which we discovered associated with oxygen utilisation. These findings highlighted the intriguing hypothesis that cell hypoxia is a crucial contributor in COPD patients' skeletal muscle.

A Switched Newton–Raphson-Based Distributed Energy Management Algorithm for Multienergy System Under Persistent DoS Attacks

The security and economy of multienergy systems (MESs) are directly threatened by the potential cyberattacks. It is of great importance to investigate the effects of cyberattacks, e.g., denial of service (DoS) attacks, on distributed energy management algorithms. To this end, this article focuses on exploring how the frequency and the time of duration of DoS attacks influence the behavior of Newton–Raphson-based distributed energy management (NRBDEM) algorithm for MES and in which condition the optimal operations can still be obtained. First, a switched NRBDEM algorithm is presented, which is composed of the normal operation mode and the attack mode. In the attack mode, the attackers are able to change the communication structure at will and make it unconnected to destroy the convergence of the switched NRBDEM algorithm. Then, by making use of automatons to generate the hybrid time domain, the switched NRBDEM algorithm is further modeled and formulated as a hybrid dynamical system, which provides a mathematical model for the subsequent convergence analysis. Therein, the generated hybrid time domain satisfies the average dwell-time constraint and time-ratio constraint to limit the persistent attacks. Furthermore, we analyze the restrained conditions for persistent attacks, under which the optimality and convergence of the switched NRBDEM algorithm can be guaranteed still. Finally, simulation results demonstrate the effectiveness of the proposed method. Note to Practitioners—The multienergy system (MES) is viewed as a typical cyber-physical system. Since it works in a networked environment, the convergence and optimality of the corresponding distributed energy management algorithms are easily destroyed by various cyberattacks, such as the DoS attack. Few noticeable studies have been documented to investigate the distributed energy management problem for MES under persistent DoS attacks. To address this issue, this article proposes a switched NRBDEM algorithm subject to persistent DoS attacks, which is made up of normal operation mode and attack mode. Moreover, sufficient conditions are derived for the tolerable frequency of attack and the time of duration. It is helpful for the practitioners to know in which conditions the global convergence and optimality can be maintained still. Several simulations are provided to verify the correctness of the proposed theoretical analysis results. Our future work will aim at analyzing the performance of different energy management algorithms under different cyberattacks.

The estimated costs and benefits of a hypothetical supervised consumption site in Providence, Rhode Island.

Overdose deaths have increased dramatically in the United States, including in Rhode Island. In July 2021, the Rhode Island government passed legislation supporting a two-year pilot program authorizing supervised consumption sites (SCSs) in response to this crisis. We estimated the costs and benefits of a hypothetical SCS in Providence, Rhode Island. We utilized a decision analytic mathematical model to compare costs and outcomes for people who inject drugs under two scenarios: (1) a SCS that includes syringe services provision, and (2) a syringe service program only (i.e., status quo). We assumed 0.95% of injections result in overdose, the SCS would serve 400 clients monthly and have a net cost of $783,899 annually, 46% of overdoses occurring outside of the SCS result in an ambulance run and 43% result in an emergency department (ED) visit, 0.79% of overdoses occurring within the SCS result in an ambulance run and ED visit, and the SCS would lead to a 25.7% reduction in fatal overdoses near the site. The model was developed from a modified societal perspective with a one-year time horizon. A hypothetical SCS in Providence would prevent approximately 2 overdose deaths, 261 ambulance runs, 244 ED visits, and 117 inpatient hospitalizations for emergency overdose care annually compared to a scenario that includes a syringe service program only. The SCS would save $1,104,454 annually compared to the syringe service program only, accounting only for facility costs and short-term costs of emergency overdose care and ignoring savings associated with averted deaths. Influential parameters included the percentage of injections resulting in overdose, the total annual injections at the SCS, and the percentage of overdoses outside of the SCS that result in an ED visit. A SCS in would result in substantial cost savings due to prevention of costly emergency overdose care.

Investigation of Brake-judder through Caliper Vibrations due to the Effects of Friction Pad Properties, Disc Thickness Variation and Brake Torque Variation using a Dynamometer

There is a budding demand in the automotive industry for discovering the causes of brake judder and numerous mathematical models for analysis and simulation have been established. Since most of the data and knowledge are hidden within automobile manufacturers, it is still a mystery to unravel and get a clear picture. Judder was reported on the field during vehicle testing with a subjective assessment of Pad A (highlighted in table 1). The aim was to investigate the problem at the brake component by altering pad grades since it was within the scope of the study. Therefore, to save the time of running the vehicles and keeping the least variables from the 4M (Material, Method, Machine, Man), 8 combinations of friction pads were taken on an inertia brake dynamometer and deals with judder arising from the disk brake assembly only. This paper provides a novel approach by running various permutations and combinations of friction pads and interlinking caliper vibrations with the factors such as Brake torque variation (BTV), disc thickness variation (DTV), and friction pad properties by DOE (Design of experiment) analysis. It also provides some insight on the causes, types of brake judder and further gives quantifiable results which determine the bandwidth of the factors based on the experimental results. The paper is structured as follows: the introduction and causes to judder are covered in section 1. Materials and methodology in section 2, Results in section 3, and conclusion in section 4.

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

In this work, the two-temperature dual-phase-lag theorem has been used to present an analytical mathematical model for calculating the vibration in a viscothermoelastic nano-resonator. The governing equations have been derived when a simply supported nano-resonator is exposed to a ramp-type thermal load and static pre-stress. The governing equations have been solved by using a direct method and obtained the solution in the Laplace transform domain where the inversions of the Laplace transform have been calculated by using the Tzou approximation method. The increments of the dynamic and conductive temperatures, volumetric deformation, and stress regarding the resonator length for various cases of temperature type, static-pre-stress, and viscothermoelastic properties with different values of ramping heat parameter have been presented in figures and studied. The parameter of the two-temperature model, static pre-stress, ramp-type heat parameter, and viscothermoelastic parameter has a significant impact on all functions studied. The ramping time parameter may be utilized to change the thermal and mechanical properties of the nano-resonator.

The Impact of the Neighborhood Built Environment on the Commuting Patterns and Health of Patients with Chronic Diseases: A Case Study of Changshu, China

The health of patients with chronic diseases is affected not only by factors such as eating and living habits, but also by the neighborhood built environment, and by travel conditions. Using 18 blocks in the main urban area of Changshu, China, we performed structural equation modelling, to explore the relationships between the neighborhood built environment, the commuting patterns of patients with chronic diseases, and patient health. We first divided the commuting patterns into four categories—walking/biking, public transportation, electric vehicles/motorcycles, and cars—and conducted a street-scale questionnaire survey. Secondly, we divided ‘health’ into three latent variables—physical health, mental health, and healthy behavior—and analyzed the factors influencing the street environment. Finally, we verified our theoretical framework through a mathematical statistical analysis model. We found that: (1) service facility, environmental quality, and community safety perception in the neighborhood built environment significantly impacted commuting patterns; (2) the patient’s physical health was significantly correlated with healthy behaviors and daily commuting patterns; and (3) socioeconomic attributes directly affected neighborhood environmental satisfaction, and indirectly affected the patient’s health. Neighborhood environmental satisfaction also directly affected the patient’s health, and there was a cross-influence relationship between these factors. We propose strengthening the walkability and connectivity of the neighborhood built environment, and improving the health awareness of patients, and their willingness to participate in healthy behaviors.

Settlement-based framework for long-term serviceability assessment of immersed tunnels

In immersed tunnels, the considerable settlement that can develop during their long-term service period may induce structural damage that affects normal operations (i.e., serviceability performance). The long-term serviceability assessment from the perspective of settlement is thusly crucial to ensure the safety of immersed tunnels, whereas a practical assessment framework is lacking to date. This study presents a feasible reliability analysis framework for the long-term serviceability assessment of immersed tunnels for the first time, in which a novel beam on elastic foundation model (BEFM) is developed as a mathematical model for tunnel settlement analysis. The BEFM is easy to be integrated into the probabilistic framework due to its simple modeling procedure and high computational efficiency. The Bayesian approach with an efficient and robust algorithm, differential evolution transitional Markov chain Monte Carlo (DE-TMCMC) algorithm is adopted to guarantee effective model calibration and uncertainty quantification. The application potential of the proposed framework is demonstrated by a case study of the Hong Kong-Zhuhai-Macao (HZM) immersed tunnel. Results show that the developed method can provide a feasible and effective assessment of the long-term serviceability of immersed tunnels, offering a practical tool to enhance the reliability and safety of immersed tunnels during their operation periods.

Closed‐form formulation of vertical dynamic response of single floating piles in homogeneous viscoelastic soil

AbstractThis paper presents a mathematical model for the elastic analysis of single floating piles subjected to axial dynamic loads, that is based on treating the soil surrounding the pile as a Tajimi‐type viscoelastic continuum. The pile and the soil column underlying the pile tip are modelled using one‐dimensional rod theory, and this allows obtaining an elegant solution that requires solving a system of linear equations, instead of complicated integral equations. Closed‐form expressions are derived for the dynamic stiffness at the pile head, and the frictional resistance along the pile shaft. The presentation concludes with a discussion on the main mechanisms that govern the inertial response of floating piles, and an investigation on the sensitivity of the dynamic stiffness and of the frictional resistance to the main geometrical and material problem parameters.

Pulling, failing, and adaptive mechanotransduction of macrophage filopodia

Macrophages use filopodia to withdraw particles toward the cell body for phagocytosis. This can require substantial forces, which the cell generates after bio-mechanical stimuli are transmitted to the filopodium. Adaptation mechanisms to mechanical stimuli are essential for cells, but can a cell iteratively improve filopodia pulling? If so, the underlying mechanic adaptation principles organized on the protein level are unclear. Here, we tackle this problem using optically trapped 1 μm beads, which we tracked interferometrically at 1 MHz during connection to the tips of dorsal filopodia of macrophages. We observe repetitive failures while the filopodium tries to pull the bead out of the optical trap. Analyses of mean bead motions and position fluctuations on the nano-meter and microsecond scale indicate mechanical ruptures caused by a force-dependent actin-membrane connection. We found that beads are retracted three times slower under any load between 5 and 40 pN relative to the no-load transport, which has the same speed as the actin retrograde flow obtained from fluorescent speckle tracking. From this duty ratio of pulling velocities, we estimated a continuous on/off binding with τoff = 2⋅τon, with measured off times τoff = 0.1–0.5 s. Remarkably, we see a gradual increase of filopodia pulling forces from 10 to 30 pN over time and after failures, which points toward an unknown adaptation mechanism. Additionally, we see that the attachment strength and friction between the bead and filopodium tip increases under load and over time. All observations are typical for catch-bond proteins such as integrin-talin complexes. We present a mechanistic picture of adaptive mechanotransduction, which formed by the help of mathematical models for repetitive tip ruptures and reconnections. The analytic mathematical model and the stochastic computer simulations, both based on catch-bond lifetimes, confirmed our measurements. Such catch-bond characteristics could also be important for other immune cells taking up counteracting pathogens.

A Simple Mathematical Model for Extreme Flood Actions on Superstructures of Coastal Bridges

Coastal bridges may be strongly affected by extreme flood actions (mainly tsunamis), which may be caused by earthquakes, volcanic eruptions, and other underwater explosions (including detonations, landslides, glaciers calvings, meteorite impacts, and other disturbances) above or below water. A simple mathematical model for analysis, processing, and easy yet effective mathematical manipulation is proposed and studied with the aid of simple principles of hydraulics, for investigating the aforementioned effects, in order to avoid rigorous analyses using ocean and coastal engineering. The main idea is based on the investigation of a water vein squirted from a height with a constant horizontal initial velocity, and the analysis of the critical wave in water veins. The results obtained, including the dynamics of deck superstructures and safety issues, reveal the critical situation for avoiding the devastating phenomena of rocking, overturning, and shifting in exemplary small and large coastal bridges. It is found that larger (longer) bridges exhibit acceptable deformations, contrary to smaller ones, while the overturning phenomenon seems to be the most critical one for both types of bridges.