IMA Journal of Applied Mathematics最新文献_第10页

A dual self-monitored reconstruction scheme on the TV-regularized inverse conductivity problem TV正则化反导问题的对偶自监测重构方案

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-04-01 DOI: 10.1093/imamat/hxab011

Vanessa Markaki;Drosos Kourounis;Antonios Charalambopoulos

{"title":"A dual self-monitored reconstruction scheme on the TV-regularized inverse conductivity problem","authors":"Vanessa Markaki;Drosos Kourounis;Antonios Charalambopoulos","doi":"10.1093/imamat/hxab011","DOIUrl":"10.1093/imamat/hxab011","url":null,"abstract":"Recently in Charalambopoulos et al. (2020), we presented a methodology aiming at reconstructing bounded total variation (\u0000<tex>$TV$</tex>\u0000) conductivities via a technique simulating the so-called half-quadratic minimization approach, encountered in Aubert & Kornprobst (2002, Mathematical Problems in Image Processing. New York, NY: Springer). The method belongs to a duality framework, in which the auxiliary function \u0000<tex>$omega (x)$</tex>\u0000 was introduced, offering a tool for smoothing the members of the admissible set of conductivity profiles. The dual variable \u0000<tex>$omega (x)$</tex>\u0000, in that approach, after every external update, served in the formation of an intermediate optimization scheme, concerning exclusively the sought conductivity \u0000<tex>$alpha (x)$</tex>\u0000. In this work, we develop a novel investigation stemming from the previous approach, having though two different fundamental components. First, we do not detour herein the \u0000<tex>$BV$</tex>\u0000-assumption on the conductivity profile, which means that the functional under optimization contains the \u0000<tex>$TV$</tex>\u0000 of \u0000<tex>$alpha (x)$</tex>\u0000 itself. Secondly, the auxiliary dual variable \u0000<tex>$omega (x)$</tex>\u0000 and the conductivity \u0000<tex>$alpha (x)$</tex>\u0000 acquire an equivalent role and concurrently, a parallel pacing in the minimization process. A common characteristic between these two approaches is that the function \u0000<tex>$omega (x)$</tex>\u0000 is an indicator of the conductivity's ‘jump’ set. A fortiori, this crucial property has been ameliorated herein, since the reciprocal role of the elements of the pair \u0000<tex>$(alpha ,omega )$</tex>\u0000 offers a self-monitoring structure very efficient to the minimization descent.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 1","pages":"604-630"},"PeriodicalIF":1.2,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imamat/hxab011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46877833","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 and pattern formation of the density-suppressed motility model 密度抑制运动模型的稳态和模式形成

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-04-01 DOI: 10.1093/imamat/hxab006

Zhi-An Wang;Xin Xu

{"title":"Steady states and pattern formation of the density-suppressed motility model","authors":"Zhi-An Wang;Xin Xu","doi":"10.1093/imamat/hxab006","DOIUrl":"10.1093/imamat/hxab006","url":null,"abstract":"This paper considers the stationary problem of density-suppressed motility models proposed in Fu et al. (2012) and Liu et al. (2011) in one dimension with Neumman boundary conditions. The models consist of parabolic equations with cross-diffusion and degeneracy. We employ the global bifurcation theory and Helly compactness theorem to explore the conditions under which non-constant stationary (pattern) solutions exist and asymptotic profiles of solutions as some parameter value is small. When the cell growth is not considered, we are able to show the monotonicity of solutions and hence achieve a global bifurcation diagram by treating the chemical diffusion rate as a bifurcation parameter. Furthermore, we show that the solutions have boundary spikes as the chemical diffusion rate tends to zero and identify the conditions for the non-existence of non-constant solutions. When transformed to specific motility functions, our results indeed give sharp conditions on the existence of non-constant stationary solutions. While with the cell growth, the structure of global bifurcation diagram is much more complicated and in particular the solution loses the monotonicity property. By treating the growth rate as a bifurcation parameter, we identify a minimum range of growth rate in which non-constant stationary solutions are warranted, while a global bifurcation diagram can still be attained in a special situation. We use numerical simulations to test our analytical results and illustrate that patterns can be very intricate and stable stationary solutions may not exist when the parameter value is outside the minimal range identified in our paper.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 1","pages":"577-603"},"PeriodicalIF":1.2,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41883152","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: 18

A method-of-lines formulation for a model of reactive settling in tanks with varying cross-sectional area 变截面储罐反应沉降模型的线性公式化方法

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-04-01 DOI: 10.1093/imamat/hxab012

Raimund Bürger;Julio Careaga;Stefan Diehl

{"title":"A method-of-lines formulation for a model of reactive settling in tanks with varying cross-sectional area","authors":"Raimund Bürger;Julio Careaga;Stefan Diehl","doi":"10.1093/imamat/hxab012","DOIUrl":"https://doi.org/10.1093/imamat/hxab012","url":null,"abstract":"Reactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular importance for the simulation and control of secondary settling tanks (SSTs) in water resource recovery facilities (WRRFs), formerly known as wastewater treatment plants. A spatially 1D model of reactive settling in an SST is formulated by combining a mechanistic model of sedimentation with compression with a model of biokinetic reactions. In addition, the cross-sectional area of the tank is allowed to vary as a function of height. The final model is a system of strongly degenerate parabolic, nonlinear partial differential equations that include discontinuous coefficients to describe the feed, underflow and overflow mechanisms, as well as singular source terms that model the feed mechanism. A finite difference scheme for the final model is developed by first deriving a method-of-lines formulation (discrete in space, continuous in time) and then passing to a fully discrete scheme by a time discretization. The advantage of this formulation is its compatibility with common practice in development of software for WRRFs. The main mathematical result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in SSTs in WRRFs illustrate the model and its discretization.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 1","pages":"514-546"},"PeriodicalIF":1.2,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imamat/hxab012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50350066","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: 5

Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles 纵向热毛细血管围绕一个稀的周期性的突出气泡垫滑动

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-04-01 DOI: 10.1093/imamat/hxab004

Ehud Yariv;Toby L Kirk

{"title":"Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles","authors":"Ehud Yariv;Toby L Kirk","doi":"10.1093/imamat/hxab004","DOIUrl":"10.1093/imamat/hxab004","url":null,"abstract":"A common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope \u0000<tex>$sigma _T$</tex>\u0000, we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width \u0000<tex>$2c$</tex>\u0000 is small compared with the array period \u0000<tex>$2l$</tex>\u0000. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation \u0000<tex>$$begin{align*}& pi frac{Gsigma_T c^2}{mu l} I(alpha), end{align*}$$</tex>\u0000 wherein \u0000<tex>$G$</tex>\u0000 is the applied-gradient magnitude, \u0000<tex>$mu $</tex>\u0000 is the liquid viscosity and \u0000<tex>$I(alpha )$</tex>\u0000, a non-monotonic function of the protrusion angle \u0000<tex>$alpha $</tex>\u0000, is provided by the quadrature, \u0000<tex>$$begin{align*}& I(alpha) = frac{2}{sinalpha} int_0^inftyfrac{sinh salpha}{ cosh s(pi-alpha) sinh s pi} , textrm{d} s. end{align*}$$</tex>","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"86 1","pages":"490-501"},"PeriodicalIF":1.2,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imamat/hxab004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48907885","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: 5

Dielectric breakdown sizes of conducting plates 导电板的介电击穿尺寸

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-04-01 DOI: 10.1093/imamat/hxab013

Mimi X Yang;Fuqian Yang;Sanboh Lee

引用次数: 1

Torsional rigidity for tangential polygons 切向多边形的扭转刚度

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-02-18 DOI: 10.1093/IMAMAT/HXAB022

G. Keady

引用次数: 1

OUP accepted manuscript OUP接受稿件

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-01-01 DOI: 10.1093/imamat/hxab037

引用次数: 0

OUP accepted manuscript OUP接受稿件

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2021-01-01 DOI: 10.1093/imamat/hxab038

引用次数: 0

Reconstruction of inclusions in electrical conductors 电导体中夹杂物的重建

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2020-11-25 DOI: 10.1093/imamat/hxaa030

M. Cristo, Giacomo Milan

引用次数: 1

Free-stream coherent structures in the unsteady Rayleigh boundary layer 非定常瑞利边界层中的自由流相干结构

IF 1.2 4区数学

IMA Journal of Applied Mathematics Pub Date : 2020-11-25 DOI: 10.1093/imamat/hxaa038

Eleanor C. Johnstone, P. Hall

引用次数: 1