A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, an...A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.展开更多
A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the...A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the anode current collector on the cell performance. Results are presented for the continuous discharge at a high rate of 1A and a moderate rate of 0.2A for a AA-sized cell. With a typical length of an anode current collector at about 70%of the cell height, the analysis showed that an increase in the length of the anode current collector would benefit the lower rate of discharge more than the higher rate of discharge.展开更多
The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of ga...The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.展开更多
Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subs...Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subsequent impact on urban structure.Considering the varying travel costs associated with electric and fuel vehicles,we analyze the dynamic choices of households concerning house locations and vehicle types in a two-dimensional monocentric city.A spatial equilibrium is developed to model the interactions between urban density,vehicle age and vehicle type.An agent-based microeconomic residential choice model dynamically coupled with a house rent market is developed to analyze household choices of home locations and vehicle energy types,considering vehicle ages and competition for public charging piles.Key findings from our proposed models show that the proportion of electric vehicles(EVs)peaks at over 50%by the end of the first scrappage period,accompanied by more than a 40%increase in commuting distance and time compared to the scenario with only fuel vehicles.Simulation experiments on a theoretical grid indicate that heterogeneity-induced residential segregation can lead to urban sprawl and congestion.Furthermore,households with EVs tend to be located farther from the city center,and an increase in EV ownership contributes to urban expansion.Our study provides insights into how individuals adapt to EV transitions and the resulting impacts on home locations and land use changes.It offers a novel perspective on the dynamic interactions between EV adoption and urban development.展开更多
Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies i...Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.展开更多
Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
A two-dimensional mathematical model was built to describe the melting process of cylindrical basalt particle bed in a crucible. The melting processes with respect to the factors of thermal boundary conditions and par...A two-dimensional mathematical model was built to describe the melting process of cylindrical basalt particle bed in a crucible. The melting processes with respect to the factors of thermal boundary conditions and particle sizes of basalt were simulated by using the numerical method (FDM). The governing equations were discretized in tridiagonal matrix form and were solved by using the tridiagonal matrix algorithm (TDMA) as well as the alternative direction implicit (ADI) solver. The temperature distribution, the moving law of the two dimensional phase-change boundaries, the thermal current distribution were given through the numerical simulation. The results provided a theoretical basis for deciding heating procedure, for evaluating power import and controlling furnace temperature and for predicting basalt melting states etc. In the experiment, an electrical furnace was designed based on the computations. It has been proved that the simulation results are reasonably coincident with the experimental data.展开更多
Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic fi...Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic field equation,energy equation,and flow equation was established.The distribution of its current density,Joule heat,flow field,and temperature field was compared and the difference of their molten metal pool was analyzed.The results show that compared with those of ESR-SE,current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip,while the Joule heat generated in the central area of the slag pool is less.In the ESR-PE,the slag flows from the outside of the electrode to the hollow area of the electrode,which makes the temperature distribution in the slag pool is more uniform.Affected by the Joule heating area and flow field,the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery.However,in the ESR-PE,the heat is concentrated near the inner and outer walls of the electrode tip,and the heat is transferred from the periphery to the center of the slag pool.The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m.Compared with that of ESR-SE,the molten metal pool of ESR-PE is shallower and flatter.展开更多
In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distributio...In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distribution for a person in a nonuniform hot environment, doing various jobs and dressed in different clothes. In addition, the results calculated from the model can be used to optimize the distribution of the tube-net lined on the WCV and to evaluate an individual thermal conditioning system with cooling water. The results obtained from the model agree well with the author's experimental data.展开更多
A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended i...A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.展开更多
G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization ...G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization of inhibitors targeting GRK2 are highly meaningful. Therefore, in order to design GRK2 inhibitors with better performance, the most active molecule was selected as a reference compound from a data set containing 4-pyridylhydrazone derivatives and triazole derivatives, and its scaffold was extracted as the initial scaffold. Then, a powerful optimization-based framework for de novo drug design, guided by binding affinity, was used to generate a virtual molecular library targeting GRK2. The binding affinity of each virtual compound in this dataset was predicted by our developed deep learning model, and the designed potential compound with high binding affinity was selected for molecular docking and molecular dynamics simulation. It was found that the designed potential molecule binds to the ATP site of GRK2, which consists of key amino acids including Arg199, Gly200, Phe202, Val205, Lys220, Met274 and Asp335. The scaffold of the molecule is stabilized mainly by H-bonding and hydrophobic contacts. Concurrently, the reference compound in the dataset was also simulated by docking. It was found that this molecule also binds to the ATP site of GRK2. In addition, its scaffold is stabilized mainly by H-bonding and π-cation stacking interactions with Lys220, as well as hydrophobic contacts. The above results show that the designed potential molecule has similar binding modes to the reference compound, supporting the effectiveness of our framework for activity-focused molecular design. Finally, we summarized the interaction characteristics of general GRK2 inhibitors and gained insight into their molecule-target binding mechanisms, thereby facilitating the expansion of lead to hit compound.展开更多
1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers ...1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.展开更多
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca...Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.展开更多
The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal...The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.展开更多
The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in t...The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.展开更多
This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O...This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.展开更多
Accurate evaluations of the burden distribution are of critical importance to stabilize the operation of blast furnace.The mathematical model and discrete element method(DEM)are two attractive methods for predicting b...Accurate evaluations of the burden distribution are of critical importance to stabilize the operation of blast furnace.The mathematical model and discrete element method(DEM)are two attractive methods for predicting burden distribution.Based on DEM,the initial velocities of the pellet,sinter,and coke were calculated,and the velocity attenuations of the above three particles between the burden and the chute were analyzed.The initial velocity and velocity attenuation were applied to a mathematical model for improving the accuracy.Additionally,based on the improved model,a scheme for rectifying the chute angles was proposed to address the fluctuation of the stock line and maintain a stable burden distribution.The validity of the scheme was confirmed via a stable burden distribution under different stock lines.The mathematical model has been successfully applied to evaluate the online burden distribution and cope with the fluctuation of the stock line.展开更多
On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely me...On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely measuring the dimensions of cutting tools during the part machining process,focusing on tool length and diameter.As a measuring instrument,the positions of the laser axis of the laser tool setter need to be accurately calibrated before use.However,in actual calibration scenarios,traditional calibration methods face challenges due to installation errors in the tool setter and geometric errors in the measuring rod.To address this issue,this study proposes a novel calibration method.Initially,the calibration mechanism of the laser beam axis is established.Based on the accurate mathematical model of the laser beam and the measuring rod,and using the polygon clipping algorithm,the mathematical mechanism of the laser tool setter’s work is established.Then,a novel method is introduced to calculate the compensation distance between the laser beam reference point and the rod bottom center point at each moment during calibration.Furthermore,by utilizing the kinematic chain of the tool setter calibration system,a new calibration method is developed to accurately calibrate the position of the laser beam axis in the machine tool coordinate system.Finally,the accuracy of the calibration method is verified through simulation experiments and calibration tests.This method improves the calibration accuracy of the tool setter,and the mathematical model of the laser tool setter can be extended to the measurement of tools,thereby improving the precision of tool measurements.This research significantly improves the efficient production performance of smart machine tools.展开更多
Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of a...Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.展开更多
HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not...HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.展开更多
文摘A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.
文摘A two-dimensional mathematical model based on the macrohomogeneous theory of porous electrodes was developed for a cylindrical Zn-MnO2 alkaline cell. The model was applied to understand the effect of the length of the anode current collector on the cell performance. Results are presented for the continuous discharge at a high rate of 1A and a moderate rate of 0.2A for a AA-sized cell. With a typical length of an anode current collector at about 70%of the cell height, the analysis showed that an increase in the length of the anode current collector would benefit the lower rate of discharge more than the higher rate of discharge.
基金the framework of the state assignment of Keldysh Institute of Applied Mathematics of RAS(Project No.125020701776-0)the Ministry of Education and Science of Russia for IO RAS(Project No.FMWE-2024-0018).
文摘The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.
基金supported by National Natural Science Foundation of China(72288101,72361137002,and 72101018)the Dutch Research Council(NWO Grant 482.22.01).
文摘Vehicle electrification,an important method for reducing carbon emissions from road transport,has been promoted globally.In this study,we analyze how individuals adapt to this transition in transportation and its subsequent impact on urban structure.Considering the varying travel costs associated with electric and fuel vehicles,we analyze the dynamic choices of households concerning house locations and vehicle types in a two-dimensional monocentric city.A spatial equilibrium is developed to model the interactions between urban density,vehicle age and vehicle type.An agent-based microeconomic residential choice model dynamically coupled with a house rent market is developed to analyze household choices of home locations and vehicle energy types,considering vehicle ages and competition for public charging piles.Key findings from our proposed models show that the proportion of electric vehicles(EVs)peaks at over 50%by the end of the first scrappage period,accompanied by more than a 40%increase in commuting distance and time compared to the scenario with only fuel vehicles.Simulation experiments on a theoretical grid indicate that heterogeneity-induced residential segregation can lead to urban sprawl and congestion.Furthermore,households with EVs tend to be located farther from the city center,and an increase in EV ownership contributes to urban expansion.Our study provides insights into how individuals adapt to EV transitions and the resulting impacts on home locations and land use changes.It offers a novel perspective on the dynamic interactions between EV adoption and urban development.
文摘Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
文摘A two-dimensional mathematical model was built to describe the melting process of cylindrical basalt particle bed in a crucible. The melting processes with respect to the factors of thermal boundary conditions and particle sizes of basalt were simulated by using the numerical method (FDM). The governing equations were discretized in tridiagonal matrix form and were solved by using the tridiagonal matrix algorithm (TDMA) as well as the alternative direction implicit (ADI) solver. The temperature distribution, the moving law of the two dimensional phase-change boundaries, the thermal current distribution were given through the numerical simulation. The results provided a theoretical basis for deciding heating procedure, for evaluating power import and controlling furnace temperature and for predicting basalt melting states etc. In the experiment, an electrical furnace was designed based on the computations. It has been proved that the simulation results are reasonably coincident with the experimental data.
基金The authors gratefully express their appreciation to Natural Science Foundation of China(No.51974153,No.U1960203)the Joint Fund of State key Laboratory of Marine Engineering and University of Science and Technology Liaoning(SKLMEA-USTLN-201901,SKLMEA-USTL-201707)the China Scholarship Council(201908210457).
文摘Taking the electroslag remelting with pipe electrode(ESR-PE)and electroslag remelting with solid electrode(ESR-SE)as the research objects,a two-dimensional steady-state mathematical model of coupled electromagnetic field equation,energy equation,and flow equation was established.The distribution of its current density,Joule heat,flow field,and temperature field was compared and the difference of their molten metal pool was analyzed.The results show that compared with those of ESR-SE,current density distribution and Joule heating area of ESR-PE are mainly concentrated in the inner and outer wall areas of the electrode tip,while the Joule heat generated in the central area of the slag pool is less.In the ESR-PE,the slag flows from the outside of the electrode to the hollow area of the electrode,which makes the temperature distribution in the slag pool is more uniform.Affected by the Joule heating area and flow field,the heat of ESR-SE is concentrated below the electrode in the slag pool area and it transfers from the center to the periphery.However,in the ESR-PE,the heat is concentrated near the inner and outer walls of the electrode tip,and the heat is transferred from the periphery to the center of the slag pool.The molten metal pool depth of ESR-SE is 0.1188 m and that of ESR-PE is 0.0962 m.Compared with that of ESR-SE,the molten metal pool of ESR-PE is shallower and flatter.
文摘In the paper a new two-dimensional 'man-WCV'(water cooling vest) mathematical model is developed. This model is of practical use: it can predict transient temperature responses and body temperature distribution for a person in a nonuniform hot environment, doing various jobs and dressed in different clothes. In addition, the results calculated from the model can be used to optimize the distribution of the tube-net lined on the WCV and to evaluate an individual thermal conditioning system with cooling water. The results obtained from the model agree well with the author's experimental data.
基金supported by the National Natural Science Foundation of China (No. 10772051)the ScienceFoundation for the Excellent Youth Scholars of Higher Education of Shanghai (No. 571215)the Research Fund for the Doctoral Program of University of Shanghai for Science and Technology(No. 10D214)
文摘A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.
基金supported by the National Natural Science Foundation of China Excellent Young Scientist Fund(22422801)the National Natural Science Foundation of China General Project(22278053)+1 种基金the National Natural Science Foundation of China General Project(22078041)Dalian High-level Talents Innovation Support Program(2023RQ059).
文摘G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization of inhibitors targeting GRK2 are highly meaningful. Therefore, in order to design GRK2 inhibitors with better performance, the most active molecule was selected as a reference compound from a data set containing 4-pyridylhydrazone derivatives and triazole derivatives, and its scaffold was extracted as the initial scaffold. Then, a powerful optimization-based framework for de novo drug design, guided by binding affinity, was used to generate a virtual molecular library targeting GRK2. The binding affinity of each virtual compound in this dataset was predicted by our developed deep learning model, and the designed potential compound with high binding affinity was selected for molecular docking and molecular dynamics simulation. It was found that the designed potential molecule binds to the ATP site of GRK2, which consists of key amino acids including Arg199, Gly200, Phe202, Val205, Lys220, Met274 and Asp335. The scaffold of the molecule is stabilized mainly by H-bonding and hydrophobic contacts. Concurrently, the reference compound in the dataset was also simulated by docking. It was found that this molecule also binds to the ATP site of GRK2. In addition, its scaffold is stabilized mainly by H-bonding and π-cation stacking interactions with Lys220, as well as hydrophobic contacts. The above results show that the designed potential molecule has similar binding modes to the reference compound, supporting the effectiveness of our framework for activity-focused molecular design. Finally, we summarized the interaction characteristics of general GRK2 inhibitors and gained insight into their molecule-target binding mechanisms, thereby facilitating the expansion of lead to hit compound.
文摘1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.
基金supported by the National Natural Science Foundation of China(11871238,11931019,12371486)。
文摘Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
文摘The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.
文摘The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.
基金The APC of this article is covered by Research Grant YUTP 015LCO-526。
文摘This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.
基金financial support from the China Minmetals Science and Technology Special Plan Foundation(2020ZXA01)the National Natural Science Foundation of China(U1960205).
文摘Accurate evaluations of the burden distribution are of critical importance to stabilize the operation of blast furnace.The mathematical model and discrete element method(DEM)are two attractive methods for predicting burden distribution.Based on DEM,the initial velocities of the pellet,sinter,and coke were calculated,and the velocity attenuations of the above three particles between the burden and the chute were analyzed.The initial velocity and velocity attenuation were applied to a mathematical model for improving the accuracy.Additionally,based on the improved model,a scheme for rectifying the chute angles was proposed to address the fluctuation of the stock line and maintain a stable burden distribution.The validity of the scheme was confirmed via a stable burden distribution under different stock lines.The mathematical model has been successfully applied to evaluate the online burden distribution and cope with the fluctuation of the stock line.
文摘On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely measuring the dimensions of cutting tools during the part machining process,focusing on tool length and diameter.As a measuring instrument,the positions of the laser axis of the laser tool setter need to be accurately calibrated before use.However,in actual calibration scenarios,traditional calibration methods face challenges due to installation errors in the tool setter and geometric errors in the measuring rod.To address this issue,this study proposes a novel calibration method.Initially,the calibration mechanism of the laser beam axis is established.Based on the accurate mathematical model of the laser beam and the measuring rod,and using the polygon clipping algorithm,the mathematical mechanism of the laser tool setter’s work is established.Then,a novel method is introduced to calculate the compensation distance between the laser beam reference point and the rod bottom center point at each moment during calibration.Furthermore,by utilizing the kinematic chain of the tool setter calibration system,a new calibration method is developed to accurately calibrate the position of the laser beam axis in the machine tool coordinate system.Finally,the accuracy of the calibration method is verified through simulation experiments and calibration tests.This method improves the calibration accuracy of the tool setter,and the mathematical model of the laser tool setter can be extended to the measurement of tools,thereby improving the precision of tool measurements.This research significantly improves the efficient production performance of smart machine tools.
文摘Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.
文摘HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.
