One-dimensional Mathematical Model Research Articles

Modelling spatio-temporal interactions between second messengers Ca and cAMP in a pancreatic -cell.

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca ), and linkages between Ca and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca levels in pancreatic -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca in -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the -cell. The model gives the individual effect of each parameter on the regulation of Ca and cAMP profiles in a -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids

A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids

Modeling mass transfer limitations driven by electrowetting in electrochemical CO2 reduction at silver gas diffusion electrodes

A one-dimensional mathematical model of a silver gas diffusion electrode (GDE) in electrochemical CO2 reduction (eCO2R) is presented. A Leverett approach is utilized to describe the coexistence of gaseous and liquid phases in the porous GDE, accounting for the potential-dependent contact angle of silver influenced by electrowetting. The model is fit to a set of experimental steady state results for sprayed electrodes with a range of diluted feeds (25−100vol%CO2). The model results ascertain a high electrolyte saturation in the GDE as the main cause for the inherent mass transfer limitations during eCO2R at elevated current densities. Furthermore, precipitation as a result of increased local K2CO3 concentration that surpasses the solubility limit is determined as degradation mechanism at current densities >3kAm−2. It is demonstrated how the model can be used to examine the effects of design parameters, indicating benefits of more hydrophobic and thinner GDEs.

Assessing dissolved oxygen dynamics in Pasig River, Philippines: A HEC-RAS modeling approach during the COVID-19 pandemic

Abstract The water quality in Pasig River has been impacted by urbanization, industrialization, and the pandemic conditions. This study involved comparative analysis of dissolved oxygen (DO) levels before and during the pandemic. Field measurements, including water temperature, salinity, and DO, were conducted during neap and spring tides. To further understand and simulate DO distribution, a one-dimensional mathematical model, specifically Hydrologic Engineering Center-River Analysis System, was employed. Results showed that DO increased during the pandemic, ranging from 3.26 to 7.25 and 1.08 to 5.69 mg/L during neap and spring tide. From the minimum standard DO level, out of eight stations, seven passed during neap tide, while one station passed during spring tide. Salinity levels were higher during spring tide, which may have affected the DO. Salt intrusion was evident until 4 km from the confluence. The hydraulic model yielded average water level differences of 5.1 and 8.3 cm during calibration and validation, respectively. The DO calibration and simulation exhibited very good statistical evaluation outcomes, with values of 0.9 for Nash-Sutcliffe Efficiency and 0.3 for Root Mean Standard Deviation Ratio. These findings hold significant potential for formulation of water quality enhancement plans and implementation of solid waste management and pollution policies.

Coupling of sediment transport phenomena with turbulent surface flows: mathematical modeling, finite volume approximation and test simulations

Several sediment transport models coupled with shallow water equations have been developed in the literature over the past few decades. The water flow in the presence of abrupt bottom slopes distorts and cause turbulence. This phenomenon is well-known in the sediment transport theory. Sediment transport models based on shallow water equations do not include turbulence effects or the phase-lag between water velocity and bottom velocity. In this study, we consider a one-dimensional free surface turbulent water flow with sediment and morphodynamic. We propose a new one-dimensional acceleration-dissipation mathematical sediment transport model that considers the distortion of horizontal profile velocity in transport. The model is an improved version of existing averaged sediment transport models. In the new model, there is a distinction between fluid velocity and bottom velocity through a new bedload equation. The mathematical model is a system of nonlinear hyperbolic partial differential equations that are approximated by a stable and robust finite volume scheme presented in the path-conservative framework. Numerical tests are performed to demonstrate the efficiency of the developed theory.

Pollution Load Coordination and Eco-Compensation for Trans-Boundary Water Pollution Control: The Case of the Tri-Border Region of the Yangtze Delta

A partitioned governance mode, in the absence of multilateral cooperation, always culminates in recurring instances of trans-boundary conflicts and critical degradation of water bodies in border regions. Addressing the existing gaps in quantitative trans-boundary pollution control research in extensive river network, a new approach was designed to strategically guide water pollution control initiatives throughout the entire tri-border region of the Yangtze Delta (TBYD) via the following steps: (1) Building upon an analysis of the trans-boundary river hydrodynamics, the tri-border effective coordination scope (TECS), i.e., a strategic coordination scope for coordinated pollution control, was delineated, and 13 county-level administrative districts were identified as effective contributing regions for detailed coordination. (2) Considering water quality standard (WQS) attainment in the trans-boundary cross-sections, a one-dimensional mathematical model covering the complex river network was established. Then, the load capacities for all the contributing administrative regions were determined to facilitate coordinated pollution load reduction across the TECS. (3) Leveraging from the sewage treatment costs within the TECS, a standardized eco-compensation criterion was established to guide the coordinated compensation practices across the TECS. (4) By comparing the practical pollution discharging amount, the coordinated load reduction rates and eco-compensation payments of all 13 contributing administrative districts for trans-boundary pollution control were assessed. These assessments will guide policy promulgation and provide quantitative data support for harmonizing pollution control policymaking and addressing intricate trans-boundary pollution issues in complex river networks.

Conflict between urbanization and water environmental protection: Lessons from the Xiangjiang River Basin in China

China, the largest developing country, has experienced rapid urbanization since its reform and opening-up. However, the increasing pollution load from urban areas has deteriorated urban river water quality, contradicting the concept of sustainable and green development promoted by the Chinese government. This situation elucidates governmental shortcomings in systematic environmental protection. Our study revealed that the current wastewater treatment plant (WWTP) discharge standards in urban areas are insufficient for attaining the desired urban river water quality and thus intensify the conflict between urbanization and water environmental protection. As urbanization continues, the urban population will grow, further exacerbating pollution and conflict. Our focus was the Xiangjiang River basin in Zunyi, a typical urbanized city in China. Using a validated one-dimensional mathematical model, we compared the water quality in the Xiangjiang River between current and upgraded WWTP discharge standards. The results showed that the water quality in the Xiangjiang River falls short of the standards, with more than 60 % of the river exceeding limits. However, upgrading WWTP discharge standards significantly reduces the proportion of river sections exceeding limits, with only 0.4 % exceeding standards during specific periods. This enhancement greatly improved the Xiangjiang River's water quality, aided in restoring the entire water environment in the basin, and supported water environmental protection goals. Our research findings offer crucial support for local governments in shaping comprehensive water environmental protection policies and insights for addressing similar environmental challenges caused by rapid urbanization in other developing regions.

Theoretical performance assessment of a multi-effect distillation system integrated with thermal vapour compression unit running on solar energy

Abstract Mathematical models can be successfully applied to predict the multi-effect distillation system integrated with thermal vapour compression unit (MED-TVC) performance under different operating conditions. In this work, a one-dimensional (1-D) mathematical model was developed to perform the theoretical analysis of a small-scale parallel feed MED-TVC desalination system driven by solar heat. A parametric study was conducted allowing the ejector motive steam temperature, first effect temperature, between effects temperature difference and ejector compression ratio to vary within an expectable range. The results showed that higher motive steam temperatures, had a positive impact on the water yield up to an optimal point. Any additional increase of driving steam temperature reduced water yield. Gain output ratio ($GOR$) was maximum at the highest considered motive temperature. It was found that the calculated specific heat transfer area does not depend on the motive temperature variation. Water yield, $GOR$ and specific heat transfer area decrease with the ejector compression ratio. The temperature difference between the evaporator effects had no effect on the water yield and $GOR$. It only decreases the specific heat transfer area. First effect temperature should be as low as possible with respect to operational constraints. Based on the parametric study, the optimal design operating conditions, corresponding to the maximum water yield is identified for a small-scale three-effect desalination system. The unit can produce up to 204 l/h drinking water with a gain output ratio of 8.6 and specific heat transfer area of 575 m2/kg/s using about 22 kW of solar heat.

Modelling sludge dewatering in treatment reed bed considering sludge deposit formation

AbstractThe accumulation of sludge deposits is a crucial factor in the dewatering efficiency of sludge treatment reed bed (STRB). This paper presents an improved one-dimensional process-based mathematical model to simulate the dewatering mechanism in STRBs, in which the compressible cake filtration (CCF) theory was implemented to simulate the sludge deposits accumulation on the surface of the reed bed, while the varying sludge deposit thickness was accounted for using the moving mesh method. The proposed model also included the dual porosity variably saturated flow model and the Penman–Monteith equation to describe the dewatering through gravity drainage and evapotranspiration, respectively. The results from the model were validated with experimental data from laboratory-scale STRBs treating septage. The simulation results showed that considering the sludge deposit layer as a specific flow resistance effectively avoids the overprediction of water infiltration rate in the reed bed. The predicted results showed excellent agreement with the actual data, where only five cases of the root mean square error were above 10% compared to the average effluent flux. Further, the effect of evapotranspiration was found to be insignificant within a short-term simulation. The consideration of the influence of sludge deposit formation on drainage dewatering using the CCF model and moving mesh model has delivered a more robust simulation for sludge dewatering in STRBs, and the proposed model is capable of facilitating the understanding of the interactions between the sludge dewatering in STRB with respect to the bed characteristics, hydraulic load, and solid load.

Semi-batch extraction of phenolic compounds from Rosmarinus officinalis: Kinetic study and dimensionless modeling

A transient and one-dimensional mathematical model with two partial differential equations is developed to simulate the extraction of de-oiled rosemary plant in a vertical fixed-bed reactor. The effect of the dimensionless numbers which appear in the final governing equations (Peclet and Damköhler numbers) is studied. The influence of solvent composition, solid particle size and temperature is also investigated. The process is controlled by internal diffusion effects, with the smallest particle size exhibiting the smallest internal diffusion coefficient. Among the different solvents, 80% ethanol shows the highest total phenolics recovery. The antiradical activity is also enhanced by increasing the temperature and the smaller particle size leads to an improvement in the extraction selectivity. Peclet number has a small effect on the results, while Damköhler number strongly affects the process. An increase in bed porosity causes a significant increase in the internal diffusion time.

Transient Process Analysis of Oscillating Motion in Oscillating Heat Pipes

Abstract During the startup phase, oscillating heat pipes (OHPs) exhibit a transient process in which the working fluid moves erratically until a steady-state oscillatory flow is attained. Understanding the transient process is important to predict how long it takes an oscillating heat pipe to reach normal operation and realize its heat transfer potential after it is started. In this paper, we perform a theoretical study of the transient process of oscillating heat pipes. Based on a one-dimensional mathematical model, we obtain an analytic solution that allows us to predict transient process characteristics of oscillating motions in an oscillating heat pipe, as well as the impact that different design and operating parameters have on this transient process.

A Tutorial on the One-Dimensional Theory of Electron-Beam Space-Charge Effect and Steady-State Virtual Cathode

The space-charge effects of pulsed high-current electron beams are very important to high-power particle beam accelerators and high-power microwave devices. The related physical phenomena have been studied for decades, and a large number of informative publications can be found in numerous scientific journals over many years. This review article is aimed at systematically summarizing most of the previous findings in a logical manner. Using a normalized one-dimensional mathematical model, analytical solutions have been obtained for the space-charge-limited current of both planar diode and drifting space. In addition, in the case of a beam current higher than the space-charge-limited current, the virtual cathode behavior and beam current reflection are quantitively studied. Furthermore, the criteria of steady-state virtual cathode formation are investigated, which leads to the physical understanding of the unstable nature of the virtual cathode. This review article is expected to serve as an integrated source of related information for young researchers and students working on high-power microwaves and pulsed particle beams.

DESIGN AND VERIFICATION OF THE MODEL OF STRUCTURE FORMATION AND HEAT TRANSFER IN A FLUIDIZED BED APPARATUS WITH A HEAT JACKET

A one-dimensional mathematical model of the formation of a fluidized bed and the evolution of its thermal state during the heating of an ensemble of particles is proposed based on the mathematical apparatus of the Markov chain theory. When describing the thermal state of the system, the processes of interfacial heat exchange between the gas flow and particles, as well as between the wall of the apparatus and the gas suspension, were taken into account. The results of previous studies and known empirical regularities for the material constants of the process were used to identify the parameters of the model. The parametric identification made it possible to adapt and apply the mathematical model for calculating the process of heat treatment of the suspension of silicate sand particles in an apparatus with a fluidized bed of a periodic principle of operation equipped with a heating jacket. Verification of the predictive capabilities of the physicomathematical model adapted in this way was carried out by comparing the forecasts obtained by calculation with the results of the full-scale experiment conducted during the study. To conduct the full-scale experiment, a sample of sand particles was placed in the apparatus, which was previously output to the established thermal regime of operation. After loading the material, a set of thermocouples equidistant from each other was placed in the apparatus and temperature readings were taken at different heights from the level of the gas distributor. The temperature distributions obtained in this way along the bed height were in good agreement with the calculated forecasts and show a significant heterogeneity of the gas phase temperature fields. The temperature of the particles was estimated only as an integral characteristic by measurements of the heat content of the bulk medium after unloading from the apparatus. The integral temperature of the particles also turned out to be close to the predicted values. In addition, during the computational and experimental study, the kinetic characteristics of the heating of the suspension of the material were clarified. Thus, the proposed mathematical model has sufficient predictive efficiency for engineering tasks and can be considered as a basis for constructing a computer method for calculating heat exchangers with a heating jacket using the fluidization technique of bulk media.

Topological optimization hybrid algorithm for the adhesive joint

The subject of this study is a topological optimization algorithm for a lapped symmetric adhesive joint. The purpose of this research is to create a hybrid optimization algorithm that combines the advantages of a genetic algorithm and a particle swarm algorithm and, at the same time, reduces the time required to solve the problem. Task: to create a methodology for solving the optimization problem for a symmetric double-sided lapped adhesive joint, which consists of a main plate and two patches (the main plate has a constant thickness, and the thickness of the patches varies along the length of the joint, this is required to reduce the stress concentration in the joint and reduce its weight) with satisfaction of the optimality criterion, namely, to minimize the mass of the structure with the strength and thickness restrictions for the patch. The optimization problem is that we must find the optimal patch form, namely, the length of the patch and the thickness-on-length dependence for the patch. Methods: the modified Goland-Reissner model was used to describe the deflected mode of the joint. The finite difference method was used to solve the direct stress state problem for the structure. For the numerical solution of the optimization problem, a combination of the multi-population model of the genetic optimization algorithm and the particle swarm algorithm was used. To improve the performance of the genetic algorithm, a multi-population model with migration of the best individuals between populations was applied. The introduction of individuals from other populations into the population avoids homogenization of the genotype in a separate population and premature stopping of the optimization process. To describe the shape of the patch, the Fourier series expansion of the patch thickness dependence was used. Results: A hybrid algorithm is proposed based on the sequential application of a genetic algorithm and a particle swarm algorithm for three populations of solutions. The particle swarm algorithm makes it possible to improve the value of the objective function achieved at the previous stage by 20%. Conclusions: the scientific novelty lies in the improvement of the optimization algorithm compared with the known ones. To reduce the calculation time, a one-dimensional adhesive joint stress state mathematical model was used in this paper. The methods used made it possible to create a combined topological optimization algorithm that combines the advantages of both methods and allows us to find a solution to the problem quite quickly. The Python program run time is only a few minutes.

Efficient Radial-Shell Model for 3D Tumor Spheroid Dynamics with Radiotherapy

Understanding the complex dynamics of tumor growth to develop more efficient therapeutic strategies is one of the most challenging problems in biomedicine. Three-dimensional (3D) tumor spheroids, reflecting avascular microregions within a tumor, are an advanced in vitro model system to assess the curative effect of combinatorial radio(chemo)therapy. Tumor spheroids exhibit particular crucial pathophysiological characteristics such as a radial oxygen gradient that critically affect the sensitivity of the malignant cell population to treatment. However, spheroid experiments remain laborious, and determining long-term radio(chemo)therapy outcomes is challenging. Mathematical models of spheroid dynamics have the potential to enhance the informative value of experimental data, and can support study design; however, they typically face one of two limitations: while non-spatial models are computationally cheap, they lack the spatial resolution to predict oxygen-dependent radioresponse, whereas models that describe spatial cell dynamics are computationally expensive and often heavily parameterized, impeding the required calibration to experimental data. Here, we present an effectively one-dimensional mathematical model based on the cell dynamics within and across radial spheres which fully incorporates the 3D dynamics of tumor spheroids by exploiting their approximate rotational symmetry. We demonstrate that this radial-shell (RS) model reproduces experimental spheroid growth curves of several cell lines with and without radiotherapy, showing equal or better performance than published models such as 3D agent-based models. Notably, the RS model is sufficiently efficient to enable multi-parametric optimization within previously reported and/or physiologically reasonable ranges based on experimental data. Analysis of the model reveals that the characteristic change of dynamics observed in experiments at small spheroid volume originates from the spatial scale of cell interactions. Based on the calibrated parameters, we predict the spheroid volumes at which this behavior should be observable. Finally, we demonstrate how the generic parameterization of the model allows direct parameter transfer to 3D agent-based models.

Mathematical model of unsteady flow in a natural circulation helium loop

This article presents a one-dimensional transient mathematical model of a helium thermosyphon, which was validated experimentally and shows agreement with measurement. The novelty stems mainly from its complexity, ability to cover real-world scenarios and a large variety of (not only) large-scale thermosyphon devices. The model uses scenario-driven boundary conditions that replicate the operation of the physical model, including the accumulation of heat energy in the solid parts of the heat exchangers and changes in mass of the flowing medium. The model is implemented using both the Eulerian fixed control volume approach and the Lagrangian particle moving approach, along with the pressure correction algorithm, which is innovative too. This paper contains a comprehensive description of the model algorithm, testing of numerical properties, such as sensibility to time step value and grid density; and the heat accumulation effect. The optimal model settings are presented. In addition, a comparison with experimental data is provided. The best agreement between model and measurement was obtained for pressure values (97% of data samples were below 5% of relative error), followed by temperature values (71% of data samples were below 5% of relative error). The model and measurement exhibited the poorest agreement in velocity values, with only 33% of data samples falling below the 5% relative error threshold.

Performance Evaluation of Different Desiccant Matrix Materials Coated with Silica Gel

ABSTRACT Excessive cooling of air is required in conventional air conditioning systems to reduce the humidity, leading to the development of desiccant wheel-based air conditioning systems. The desiccant wheel consists of desiccant material which is deposited on matrix material. In this study, aluminum, magnesium alloy, Teflon and fiberglass have been considered matrix materials of the desiccant wheel. A one-dimensional mathematical model has been developed to evaluate the effect of these matrix materials. The results show that fiberglass can be selected as a suitable matrix material for drying applications because it has maximum moisture removal (1.92 g/kg) and temperature difference (4.72 °C) at optimal rotational speed, which are desirable for drying. While aluminum can be selected as a suitable matrix material for air conditioning applications because, at the optimal rotational speed, it has lower maximum moisture removal (1.26 g/kg) and temperature difference (3.14 °C) as compared to other matrix materials. As moderate maximum moisture removal and lower temperature difference are the requirements for air conditioning. A similar trend of results has been also obtained for other parameters (volume ratio, regeneration velocity, regeneration temperature, etc.) of this study.

The current state of Lake Dålk (Larsemann Hills, East Antarctica)

The study focuses on the current state of englacial Lake Dålk (Larsemann Hills Oasis), which was completely devastated in January 2017 by a catastrophic outburst and formed again in February 2020. A set of works including ground-penetrating radar (GPR) profiling, geodetic survey, core drilling, thermometric measurements and isotopic analysis was performed. As a result, new data were obtained about the modern boundaries of the reservoir, ice thickness and depths, as well as about the peculiarities of freezing of the lake after re-formation. Based on the field data obtained, one-dimensional mathematical modeling of Lake Dålk freezing was carried out, the results of which showed further scenarios of its evolution.

Investigation of Heat and Mass Transfer in the Process of Fuel Preparation from Biomass Particles with High Moisture

Currently, in a number of countries an urgent task for development of fuel and energy complexes is to increase the share of generation by involving solid fuels in circulation. Among such projects, those that allow the disposal of waste from various industries are particularly significant. Expired food products in this context are represented as a renewable local energy resource. However, such products require serious activities to prepare them for incineration or other type of high-temperature processing in order to obtain energy. The purpose of the present work is to improve methods of preparing fuel from recycled carrot fruits (unsuitable for use in the food sector). During the fuel preparation of carrots, the drying stage is limiting for the rational organization of its processing in boilers. In addition, the drying stage is extremely energy-consuming, so reliable prediction of its kinetics largely determines the efficiency of the entire technological process. In the course of the study, the following tasks were solved: a numerical method was developed for describing the processes of internal and external heat and mass transfer problems using an explicit difference approximation of differential equations of heat and mass transfer; parametric identification of the proposed one-dimensional mathematical model was performed using empirical dependencies known from literature sources; empirical verification of the proposed mathematical model was carried out by comparing the calculated forecasts obtained with the results of their own field experiments. The fact that the proposed mathematical model and the results of the full-scale experiment are independent, while the calculated forecasts and experimental data are in good agreement, makes us possible to consider the proposed calculation method as a reliable scientific basis for a computer method for calculating of heat and mass transfer processes when organizing the preparation of fuel from carrot fruits.

Topological optimization BI-adhesive double lap adhesive joint. One-dimension model

The aim of the article is to construct a solution to the problem of topological optimization of a symmetric two-shear and bi-adhesive joint. The one-dimensional mathematical model of the stress state of a symmetrical double-shear adhesive joint with a variable thickness of the outer substrate along the lap length is represented in the article. The proposed model is a generalization of the classical Goland-Reissner model. The proposed mathematical model is used to solve the problem of topological optimization of the outer substrate shape as well as to obtain the optimal length of the sections for the rigid and compliant adhesives. The expansion of the outer substrate thickness dependence along the adhesive joint length into a Fourier series in cosines was used to describe the shape of the outer substrate. The desired values in the optimization problem are the lengths of the adhesive joint sections with the compliant and rigid adhesives as well as the Fourier coefficients. The objective function is the cross-sectional area of the outer substrate. Restrictions are imposed on the maximum stresses in the adhesive layer and in the outer substrate. A genetic algorithm was used to solve the optimization problem. The direct problem of determining the stress state of the adhesive joint at specified parameters was solved using the finite difference method. The model problem is solved and the results of the stress state calculation are compared with the results of finite element modeling.