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Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation 基于图像的运动估计中促进发散自由流的参数方法及其在生物灌溉中的应用
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-06-15 DOI: 10.1017/s095679252200016x
N. Santitissadeekorn, C. Meile, E. Bollt, G. Waldbusser
{"title":"Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation","authors":"N. Santitissadeekorn, C. Meile, E. Bollt, G. Waldbusser","doi":"10.1017/s095679252200016x","DOIUrl":"https://doi.org/10.1017/s095679252200016x","url":null,"abstract":"Flow fields are determined from image sequences obtained in an experiment in which benthic macrofauna, Arenicola marina, causes water flow and the images depict the distribution of a tracer that is carried with the flow. The experimental setup is such that flow is largely two-dimensional, with a localised region where the Arenicola resides, from which flow originates. Here, we propose a novel parametric framework that quantifies such flow that is dominant along the image plane. We adopt a Bayesian framework so that we can impart certain physical constraints on parameters into the estimation process via prior distribution. The primary aim is to approximate the mean of the posterior distribution to present the parameter estimate via Markov Chain Monte Carlo. We demonstrate that the results obtained from the proposed method provide more realistic flows (in terms of divergence magnitude) than those computed from classical approaches such as the multi-resolution Horn–Schunk method. This highlights the usefulness of our approach if motion is largely constrained to the image plane with localised fluid sources.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"10 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41297272","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
Dynamics and steady state of squirmer motion in liquid crystal 液晶中蠕动运动的动力学与稳态
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-06-13 DOI: 10.1017/s0956792523000177
L. Berlyand, Haiyang Chi, M. Potomkin, N. Yip
{"title":"Dynamics and steady state of squirmer motion in liquid crystal","authors":"L. Berlyand, Haiyang Chi, M. Potomkin, N. Yip","doi":"10.1017/s0956792523000177","DOIUrl":"https://doi.org/10.1017/s0956792523000177","url":null,"abstract":"\u0000 We analyse a nonlinear partial differential equation system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer’s motility, the squirmer model is used in which self-propulsion enters the model through the slip velocity on the microswimmer’s surface. The liquid crystal is described using the well-established Beris–Edwards formulation. In previous computational studies, it was shown that the squirmer, regardless of its initial configuration, eventually orients itself either parallel or perpendicular to the preferred orientation dictated by the liquid crystal. Furthermore, the corresponding solution of the coupled nonlinear system converges to a steady state. In this work, we rigorously establish the existence of steady state and also the finite-time existence for the time-dependent problem in a periodic domain. Finally, we will use a two-scale asymptotic expansion to derive a homogenised model for the collective swimming of squirmers as they reach their steady-state orientation and speed.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49277964","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
Steady states of thin-film equations with van der Waals force with mass constraint 具有质量约束的范德华力薄膜方程的稳态
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-05-30 DOI: 10.1017/s0956792522000134
Xinfu Chen, Huiqiang Jiang, Guoqing Liu
{"title":"Steady states of thin-film equations with van der Waals force with mass constraint","authors":"Xinfu Chen, Huiqiang Jiang, Guoqing Liu","doi":"10.1017/s0956792522000134","DOIUrl":"https://doi.org/10.1017/s0956792522000134","url":null,"abstract":"We consider steady states with mass constraint of the fourth-order thin-film equation with van der Waals force in a bounded domain which leads to a singular elliptic equation for the thickness with an unknown pressure term. By studying second-order nonlinear ordinary differential equation, \u0000\u0000 \u0000 \u0000 \u0000begin{equation*}h_{rr}+frac{1}{r}h_{r}=frac{1}{alpha}h^{-alpha}-pend{equation*}\u0000\u0000 \u0000 we prove the existence of infinitely many radially symmetric solutions. Also, we perform rigorous asymptotic analysis to identify the blow-up limit when the steady state is close to a constant solution and the blow-down limit when the maximum of the steady state goes to the infinity.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761642","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
Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation 显著(1+2)维Fokker-Planck方程的扩展对称性分析
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-05-26 DOI: 10.1017/S0956792523000074
Serhii D. Koval, Alexander Bihlo, R. Popovych
{"title":"Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation","authors":"Serhii D. Koval, Alexander Bihlo, R. Popovych","doi":"10.1017/S0956792523000074","DOIUrl":"https://doi.org/10.1017/S0956792523000074","url":null,"abstract":"Abstract We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker–Planck equations by its remarkable symmetry properties. In particular, its essential Lie invariance algebra is eight-dimensional, which is the maximum dimension within the above class. We compute the complete point symmetry pseudogroup of the Fokker–Planck equation using the direct method, analyse its structure and single out its essential subgroup. After listing inequivalent one- and two-dimensional subalgebras of the essential and maximal Lie invariance algebras of this equation, we exhaustively classify its Lie reductions, carry out its peculiar generalised reductions and relate the latter reductions to generating solutions with iterative action of Lie-symmetry operators. As a result, we construct wide families of exact solutions of the Fokker–Planck equation, in particular, those parameterised by an arbitrary finite number of arbitrary solutions of the (1+1)-dimensional linear heat equation. We also establish the point similarity of the Fokker–Planck equation to the (1+2)-dimensional Kramers equations whose essential Lie invariance algebras are eight-dimensional, which allows us to find wide families of exact solutions of these Kramers equations in an easy way.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"1067 - 1098"},"PeriodicalIF":1.9,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45550127","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: 4
A distributionally ambiguous two-stage stochastic approach for investment in renewable generation 可再生能源发电投资的一种分布模糊两阶段随机方法
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-05-12 DOI: 10.1017/S0956792522000122
Pedro Borges, C. Sagastizábal, M. Solodov, A. Tomasgard
{"title":"A distributionally ambiguous two-stage stochastic approach for investment in renewable generation","authors":"Pedro Borges, C. Sagastizábal, M. Solodov, A. Tomasgard","doi":"10.1017/S0956792522000122","DOIUrl":"https://doi.org/10.1017/S0956792522000122","url":null,"abstract":"The optimal expansion of a power system with reduced carbon footprint entails dealing with uncertainty about the distribution of the random variables involved in the decision process. Optimisation under ambiguity sets provides a mechanism to suitably deal with such a setting. For two-stage stochastic linear programs, we propose a new model that is between the optimistic and pessimistic paradigms in distributionally robust stochastic optimisation. When using Wasserstein balls as ambiguity sets, the resulting optimisation problem has nonsmooth convex constraints depending on the number of scenarios and a bilinear objective function. We propose a decomposition method along scenarios that converges to a solution, provided a global optimisation solver for bilinear programs with polyhedral feasible sets is available. The solution procedure is applied to a case study on expansion of energy generation that takes into account sustainability goals for 2050 in Europe, under uncertain future market conditions.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"484 - 504"},"PeriodicalIF":1.9,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42229414","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
Asymptotic and transient dynamics of SEIR epidemic models on weighted networks 加权网络上SEIR流行病模型的渐近和瞬态动力学
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-04-26 DOI: 10.1017/s0956792522000109
CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN
{"title":"Asymptotic and transient dynamics of SEIR epidemic models on weighted networks","authors":"CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN","doi":"10.1017/s0956792522000109","DOIUrl":"https://doi.org/10.1017/s0956792522000109","url":null,"abstract":"<p>We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"67 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539755","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
Asymptotic and transient dynamics of SEIR epidemic models on weighted networks 加权网络上SEIR流行病模型的渐近和瞬态动力学
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-04-26 DOI: 10.1017/s0956792522000109
CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN
{"title":"Asymptotic and transient dynamics of SEIR epidemic models on weighted networks","authors":"CANRONG TIAN, ZUHAN LIU, SHIGUI RUAN","doi":"10.1017/s0956792522000109","DOIUrl":"https://doi.org/10.1017/s0956792522000109","url":null,"abstract":"<p>We study the effect of population mobility on the transmission dynamics of infectious diseases by considering a susceptible-exposed-infectious-recovered (SEIR) epidemic model with graph Laplacian diffusion, that is, on a weighted network. First, we establish the existence and uniqueness of solutions to the SEIR model defined on a weighed graph. Then by constructing Liapunov functions, we show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. Finally, we apply our generalized weighed graph to Watts–Strogatz network and carry out numerical simulations, which demonstrate that degrees of nodes determine peak numbers of the infectious population as well as the time to reach these peaks. It also indicates that the network has an impact on the transient dynamical behaviour of the epidemic transmission.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"67 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539749","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
Steady state diffusion in tubular structures: Assessment of one-dimensional models 管状结构的稳态扩散:一维模型的评估
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-04-25 DOI: 10.1017/s0956792522000110
P. A. MARTIN, A. T. SKVORTSOV
{"title":"Steady state diffusion in tubular structures: Assessment of one-dimensional models","authors":"P. A. MARTIN, A. T. SKVORTSOV","doi":"10.1017/s0956792522000110","DOIUrl":"https://doi.org/10.1017/s0956792522000110","url":null,"abstract":"<p>Steady-state diffusion in long axisymmetric structures is considered. The goal is to assess one-dimensional approximations by comparing them with axisymmetric eigenfunction expansions. Two problems are considered in detail: a finite tube with one end that is partly absorbing and partly reflecting; and two finite coaxial tubes with different cross-sectional radii joined together abruptly. Both problems may be modelled using effective boundary conditions, containing a parameter known as the trapping rate. We show that trapping rates depend on the lengths of the finite tubes (and that they decay slowly as these lengths increase) and we show how trapping rates are related to blockage coefficients, which are well known in the context of potential flow along tubes of infinite length.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"117 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539677","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
Steady state diffusion in tubular structures: Assessment of one-dimensional models 管状结构的稳态扩散:一维模型的评估
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-04-25 DOI: 10.1017/s0956792522000110
P. A. MARTIN, A. T. SKVORTSOV
{"title":"Steady state diffusion in tubular structures: Assessment of one-dimensional models","authors":"P. A. MARTIN, A. T. SKVORTSOV","doi":"10.1017/s0956792522000110","DOIUrl":"https://doi.org/10.1017/s0956792522000110","url":null,"abstract":"<p>Steady-state diffusion in long axisymmetric structures is considered. The goal is to assess one-dimensional approximations by comparing them with axisymmetric eigenfunction expansions. Two problems are considered in detail: a finite tube with one end that is partly absorbing and partly reflecting; and two finite coaxial tubes with different cross-sectional radii joined together abruptly. Both problems may be modelled using effective boundary conditions, containing a parameter known as the trapping rate. We show that trapping rates depend on the lengths of the finite tubes (and that they decay slowly as these lengths increase) and we show how trapping rates are related to blockage coefficients, which are well known in the context of potential flow along tubes of infinite length.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"117 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539730","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
On the Lie symmetries of characteristic function hierarchy in compressible turbulence 关于可压缩湍流中特征函数层次的Lie对称性
IF 1.9 4区 数学
European Journal of Applied Mathematics Pub Date : 2022-04-11 DOI: 10.1017/S0956792522000092
D. S. Praturi, D. Plümacher, M. Oberlack
{"title":"On the Lie symmetries of characteristic function hierarchy in compressible turbulence","authors":"D. S. Praturi, D. Plümacher, M. Oberlack","doi":"10.1017/S0956792522000092","DOIUrl":"https://doi.org/10.1017/S0956792522000092","url":null,"abstract":"We compute the Lie symmetries of characteristic function (CF) hierarchy of compressible turbulence, ignoring the effects of viscosity and heat conductivity. In the probability density function (PDF) hierarchy, a typical non-local nature is observed, which is naturally eliminated in the CF hierarchy. We observe that the CF hierarchy retains all the symmetries satisfied by compressible Euler equations. Broadly speaking, four types of symmetries can be discerned in the CF hierarchy: (i) symmetries corresponding to coordinate system invariance, (ii) scaling/dilation groups, (iii) projective groups and (iv) statistical symmetries, where the latter define measures of intermittency and non-gaussianity. As the multi-point CFs need to satisfy additional constraints such as the reduction condition, the projective symmetries are only valid for monatomic gases, that is, the specific heat ratio, \u0000$gamma = 5/3$\u0000 . The linearity of the CF hierarchy results in the statistical symmetries due to the superposition principle. For all of the symmetries, the global transformations of the CF and various key compressible statistics are also presented.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"34 1","pages":"913 - 935"},"PeriodicalIF":1.9,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47759059","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
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