Mathematical Modelling of Natural Phenomena最新文献_第8页

Mathematical modelling of proton migration in Earth mantle 地幔中质子迁移的数学模型

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-05-17 DOI: 10.1051/mmnp/2022018

V. Bobrovskiy, J. Galvis, A. Kaplin, A. Sinitsyn, Marco Tognoli, P. Trucco

{"title":"Mathematical modelling of proton migration in Earth mantle","authors":"V. Bobrovskiy, J. Galvis, A. Kaplin, A. Sinitsyn, Marco Tognoli, P. Trucco","doi":"10.1051/mmnp/2022018","DOIUrl":"https://doi.org/10.1051/mmnp/2022018","url":null,"abstract":"In the study, we address the mathematical problem of proton migration in the Earth’s\u0000mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic\u0000proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x,t) and then reconstructing the distribution function f(x, v, t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45420879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos 基于多项式混沌的流行病模型的有效不确定性量化和方差敏感性分析

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-25 DOI: 10.1051/mmnp/2022014

Bjørn Jensen, A. Engsig-Karup, Kim Knudsen

{"title":"Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos","authors":"Bjørn Jensen, A. Engsig-Karup, Kim Knudsen","doi":"10.1051/mmnp/2022014","DOIUrl":"https://doi.org/10.1051/mmnp/2022014","url":null,"abstract":"The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41974327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Immuno-epidemiological model-based prediction of further COVID-19 epidemic outbreaks due to immunity waning 基于免疫流行病学模型的COVID-19疫情预测

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-22 DOI: 10.1051/mmnp/2022017

Samiran Ghosh, M. Banerjee, V. Volpert

引用次数: 9

A MULTIPLE TIMESCALE NETWORK MODEL OF INTRACELLULARCALCIUM CONCENTRATIONS IN COUPLED NEURONS: INSIGHTS FROMROM SIMULATIONS. 耦合神经元细胞内钙浓度的多时间尺度网络模型:来自模拟的见解。

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-18 DOI: 10.1051/mmnp/2022016

Alejandro BANDERA MORENO, Macarena Gómez-Mármol, S. Fernández-García, A. Vidal

{"title":"A MULTIPLE TIMESCALE NETWORK MODEL OF INTRACELLULAR\u0000CALCIUM CONCENTRATIONS IN COUPLED NEURONS: INSIGHTS FROM\u0000ROM SIMULATIONS.","authors":"Alejandro BANDERA MORENO, Macarena Gómez-Mármol, S. Fernández-García, A. Vidal","doi":"10.1051/mmnp/2022016","DOIUrl":"https://doi.org/10.1051/mmnp/2022016","url":null,"abstract":"In [16], the authors analyzed the synchronization features between two identical 3D slow-fast oscillators, symmetrically coupled, built as an extension of the FitzHugh–Nagumo dynamics generating Mixed-Mode Oscillations. The third variable, which is slow, represents the intracellular calcium concentration in neurons. Here, we consider an extension of this model in two directions. First, we consider heterogeneity among cells and analyze the coupling of two oscillators with different values for one parameter tuning the intrinsic frequency. We identify new patterns of antiphasic synchronization, with non-trivial signatures and that exhibit a Devil’s Staircase phenomenon in transitions. Second, we introduce a network of N cells divided into two clusters: the coupling between neurons in each cluster is excitatory, while between the two clusters is inhibitory. Such system models the interactions between neurons tending to synchronization in two subpopulations inhibiting each other, like ipsi- and contra-lateral motoneurons assemblies. To perform the numerical simulations when N is large, as an initial step towards the network analysis, we consider Reduced Order Models to save computational costs. We present the numerical reduction results in a network of 100 cells. To validate the numerical reduction method, we compare the outputs and CPU times obtained in different cases.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41945418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Study of architectural forms of invasive carcinoma based on the measurement of pattern complexity 基于模式复杂性测量的浸润性癌结构形态研究

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-13 DOI: 10.1051/mmnp/2022013

D. Bratsun, I. Krasnyakov

{"title":"Study of architectural forms of invasive carcinoma based on the measurement of pattern complexity","authors":"D. Bratsun, I. Krasnyakov","doi":"10.1051/mmnp/2022013","DOIUrl":"https://doi.org/10.1051/mmnp/2022013","url":null,"abstract":"Several years ago, a new paradigm of cancer perception emerged, considering a tumor not as a senseless heap of cells but as a self-organizing heterogeneous tissue of cancer cells that collectively fight for survival. It implies that the architectural forms that a tumor takes during its growth are not occasional but are a synergistic response of a group of cancer cells in competition for the organism’s resources. In this work, we generate various patterns of a two-dimensional tumor using our previously developed individual-based model mimicking carcinoma features. Every cell is represented by a polygon dynamically changing its form and size. The dynamics of tissue are governed by the elastic potential energy. We numerically obtain various patterns of carcinoma and estimate empirical spatial entropy and complexity measures applying the approach based on the fast finite shearlet transform. We show how the complexity of growing carcinoma changes over time and depending on the values of the cell intercalation parameters. In each case, we give a rational explanation of why this form is beneficial to the tumor. Our results show that one can use complexity measurements for quantitative classification of tumors obtained in silico , which potentially could find its application in practice.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49206254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Optimal Control Strategy to Control Pandemic COVID-19 Using MSI_LI_HR_V Model 基于MSI_LI_HR_V模型的大流行COVID-19最优控制策略

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-12 DOI: 10.1051/mmnp/2022015

S. S. Chaharborj, Jalal Hassanzadeh Asl, Babak Mohammadi

{"title":"Optimal Control Strategy to Control Pandemic COVID-19 Using MSI_LI_HR_V Model","authors":"S. S. Chaharborj, Jalal Hassanzadeh Asl, Babak Mohammadi","doi":"10.1051/mmnp/2022015","DOIUrl":"https://doi.org/10.1051/mmnp/2022015","url":null,"abstract":"Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobin matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model’s stability and unstability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of Covid-19 from 4 Jan, 2021 up to 14 June, 2021 in Iran.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46572690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Protein pattern formation induced by the joint effect of noise and delay in a multi-cellular system 多细胞系统中由噪声和延迟共同作用诱导的蛋白质模式形成

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-04 DOI: 10.1051/mmnp/2022011

D. Bratsun

{"title":"Protein pattern formation induced by the joint effect of noise and delay in a multi-cellular system","authors":"D. Bratsun","doi":"10.1051/mmnp/2022011","DOIUrl":"https://doi.org/10.1051/mmnp/2022011","url":null,"abstract":"We explore the combined effect of the intrinsic noise and time delay on the spatial pattern formation within the framework of a multi-scale mobile lattice model mimicking two-dimensional epithelium tissues. Every cell is represented by an elastic polygon changing its form and size under pressure from the surrounding cells. The model includes the procedure of minimization of the potential energy of tissue. The protein fluctuations in the tissue are driven by transcription/translation processes in cells exchanging chemical and mechanical signals. Network architecture includes an autorepressor model with time-delayed negative feedback with the only gene defining oscillations. Simultaneously, the expressed protein of the autorepressor acts as a positive regulator of the signaling protein by activating its transcription. The signaling species is assumed to spread from one cell to the other by the diffusion mechanism. We provide both deterministic and stochastic descriptions. The numerical simulation of spatially-extended stochastic oscillations is performed using a generalized Gillespie algorithm. We developed this method earlier to account for the non-Markovian properties of random biochemical events with delay. Finally, we demonstrate that time delay, intrinsic noise, and spatial signaling can cause a system to develop the protein pattern even when its deterministic counterpart exhibits no pattern formation.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48087857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Mathematical Modeling of Aphron Drilling nanofluid Driven by Electroosmotically Modulated Peristalsis Through a Pipe 电渗调节蠕动驱动Aphron钻井纳米流体的数学模型

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-04-03 DOI: 10.1051/mmnp/2022012

J. Akram, Noreen Sher Akbar

{"title":"Mathematical Modeling of Aphron Drilling nanofluid Driven by Electroosmotically Modulated Peristalsis Through a Pipe","authors":"J. Akram, Noreen Sher Akbar","doi":"10.1051/mmnp/2022012","DOIUrl":"https://doi.org/10.1051/mmnp/2022012","url":null,"abstract":"This analysis is conducted for a theoretical examination of the fluid flow characteristics and heat transferred by the nanoparticle-enhanced drilling muds flowing through drilling pipes under various physical conditions. Here, an important type of drilling fluid called Aphron drilling fluid is under consideration which is very effective for drilling in depleted regions. The rheological characteristics of the drilling fluid are predicted by Herschel-Bulkley fluid model. The fluid flow is driven by peristaltic pumping which is further aided by electroosmosis. The zinc oxide nanoparticles are dispersed in the aphron drilling fluid to prepare the nanofluid. The administering set of equations are simplified under the lubrication approach and the closed-form solutions are obtained for velocity and pressure gradient force. However, numerical solutions are executed for the temperature of nanofluid through built-in routine bvp4c of MATLAB. Fluid flow characteristics are analyzed for variation in physical conditions through graphical results. The outcomes of this study reveal that velocity profile substantially rises for application of forwarding electric field and temperature profile significantly decays in this case. An increment in temperature difference raises the magnitude of the Nusselt number. Furthermore, the nanoparticle volume fraction contributes to fluid acceleration and thermal conductivity of the drilling fluid.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44054473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bi-domain model 躯干耦合双域模型强T-周期解的Faedo-Galerkin近似的强收敛性

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-03-14 DOI: 10.1051/mmnp/2023012

Raúl Felipe-Sosa, A. Fraguela-Collar, Yofre H. Garc'ia G'omez

引用次数: 0

Concentration and cavitation in the vanishing pressure limit of solutions to a 3 × 3 generalized Chaplygin gas equations 3 × 3广义Chaplygin气体方程解的消失压力极限中的浓度和空化

IF 2.2 4区数学

Mathematical Modelling of Natural Phenomena Pub Date : 2022-03-07 DOI: 10.1051/mmnp/2022009

Yu Zhang, S. Fan, Yanyan Zhang

{"title":"Concentration and cavitation in the vanishing pressure limit of solutions to a 3 × 3 generalized Chaplygin gas equations","authors":"Yu Zhang, S. Fan, Yanyan Zhang","doi":"10.1051/mmnp/2022009","DOIUrl":"https://doi.org/10.1051/mmnp/2022009","url":null,"abstract":"The phenomena of concentration and cavitation are identified and analyzed by studying the vanishing pressure limit of solutions to the 3×3 isentropic compressible Euler equations for generalized Chaplygin gas (GCG) with a small parameter. It is rigorously proved that, any Riemann solution containing two shocks and possibly one-contact-discontinuity of the GCG equations converges to a delta-shock solution of the same system as the parameter decreases to a certain critical value. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the limiting solution is just the delta-shock solution of the pressureless gas dynamics (PGD) model, and the intermediate density between the two shocks tends to a weighted δ -measure that forms the delta shock wave; any Riemann solution containing two rarefaction waves and possibly one contact-discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some numerical results are presented to exhibit the processes of concentration and cavitation as the pressure decreases.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48697441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0