Results in Applied Mathematics最新文献

{"title":"A coupled high-accuracy phase-field fluid–structure interaction framework for Stokes fluid-filled fracture surrounded by an elastic medium","authors":"Henry von Wahl ,&nbsp;Thomas Wick","doi":"10.1016/j.rinam.2024.100455","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100455","url":null,"abstract":"<div><p>In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid–structure interaction. The key motivation is to utilise phase-field modelling to compute the fracture path. A mesh reconstruction allows a switch from interface-capturing to interface-tracking in which the coupling conditions can be realised in a highly accurate fashion. Consequently, inside the fracture, a Stokes flow can be modelled that is coupled to the surrounding elastic medium. A fully coupled approach is obtained by iterating between the phase-field and the fluid–structure interaction model. The resulting algorithm is demonstrated for several numerical examples of quasi-static brittle fractures. We consider both stationary and quasi-stationary problems. In the latter, the dynamics arise through an incrementally increasing given pressure.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100455"},"PeriodicalIF":2.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000256/pdfft?md5=d27201dc0b601b2f899490af0fb0795c&pid=1-s2.0-S2590037424000256-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140551610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Upper Bound of Near Potential Differential Games","authors":"Balint Varga","doi":"10.1016/j.rinam.2024.100453","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100453","url":null,"abstract":"<div><p>This letter presents an extended analysis and a novel upper bound of the subclass of Linear Quadratic Near Potential Differential Games (LQ NPDG). LQ NPDGs are a subclass of potential differential games, for which there is a distance between an LQ exact potential differential game and the LQ NPDG. LQ NPDGs exhibit a unique characteristic: The smaller the distance from an LQ exact potential differential game, the more closer their dynamic trajectories. This letter introduces a novel upper bound for this distance. Moreover, a linear relation between this distance and the resulting trajectory errors is established, opening the possibility for further application of LQ NPDGs.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100453"},"PeriodicalIF":2.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000232/pdfft?md5=ab9c4fddd1098daffbde300c81a0c9f6&pid=1-s2.0-S2590037424000232-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140550339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis on nonlinear differential equation with a deviating argument via Faedo–Galerkin method","authors":"M. Manjula ,&nbsp;E. Thilakraj ,&nbsp;P. Sawangtong ,&nbsp;K. Kaliraj","doi":"10.1016/j.rinam.2024.100452","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100452","url":null,"abstract":"<div><p>This article focuses on the impulsive fractional differential equation (FDE) of Sobolev type with a nonlocal condition. Existence and uniqueness of the approximations are determined via analytic semigroup and fixed point method. Convergence’s approximation is demonstrated by the idea of fractional power of a closed linear operator. Using an approximation procedure, a novel approach is reached. An illustration is used to clarify our key findings.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100452"},"PeriodicalIF":2.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000220/pdfft?md5=06f3a022546581dab00d18fcb1040308&pid=1-s2.0-S2590037424000220-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140546321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global boundedness and asymptotic behavior of the chemotaxis system for alopecia areata with singular sensitivity","authors":"Peng Gao ,&nbsp;Lu Xu","doi":"10.1016/j.rinam.2024.100450","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100450","url":null,"abstract":"&lt;div&gt;&lt;p&gt;This paper is concerned with a three-component chemotaxis system for alopecia areata with singular sensitivity &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;under the homogeneous Neumann boundary conditions in a smoothly bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100450"},"PeriodicalIF":2.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000207/pdfft?md5=2ce9c6cd1fc48d777a643ef5b1e29b62&pid=1-s2.0-S2590037424000207-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140533856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bernstein polynomials method for solving multi-order fractional neutral pantograph equations with error and stability analysis","authors":"M.H.T. Alshbool","doi":"10.1016/j.rinam.2024.100451","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100451","url":null,"abstract":"<div><p>In this investigation, we present a new method for addressing fractional neutral pantograph problems, utilizing the Bernstein polynomials method. We obtain solutions for the fractional pantograph equations by employing operational matrices of differentiation, derived from fractional derivatives in the Caputo sense applied to Bernstein polynomials. Error analysis, along with Chebyshev algorithms and interpolation nodes, is employed for solution characterization. Both theoretical and practical stability analyses of the method are provided. Demonstrative examples indicate that our proposed techniques occasionally yield exact solutions. We compare the algorithms using several established analytical methods. Our results reveal that our algorithm, based on Bernstein series solution methods, outperforms others, exhibiting superior performance with higher accuracy orders compared to those obtained from Chebyshev spectral methods, Bernoulli wavelet method, and Spectral Tau method.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100451"},"PeriodicalIF":2.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000219/pdfft?md5=ab06e37e6cd3f1424460dd1b0b8627ac&pid=1-s2.0-S2590037424000219-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140533857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decay analysis of bivariate Chebyshev coefficients for functions with limited regularity","authors":"Akansha","doi":"10.1016/j.rinam.2024.100449","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100449","url":null,"abstract":"<div><p>The Chebyshev polynomial approximation is a useful tool to approximate smooth and non-smooth functions. In fact, for a sufficiently smooth function, the partial sum of Chebyshev series expansion provides optimal polynomial approximation. Moreover, because the construction of these polynomial approximations is computational efficient, they are widely used in numerical schemes for solving partial deferential equations. Significant efforts have been devoted to establishing decay bounds for series coefficients, including Chebyshev, Jacobi, and Legendre series, for both smooth and non-smooth univariate functions. However, the literature lacks similar estimates for bivariate functions. This paper aims to address this gap by examining the decay estimates of bivariate Chebyshev coefficients, contributing both theoretically and practically to the understanding and application of Chebyshev series expansions, especially concerning functions with limited smoothness. Additionally, we derive <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-error estimates for the partial sum of Chebyshev series expansions of functions with bounded Vitali variation. Furthermore, we provide an estimate for the discrepancy between exact and approximated Chebyshev coefficients, leveraging a quadrature formula. This analysis leads to the deduction of an asymptotic <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-approximation error for finite partial sums of Chebyshev series with approximated coefficients.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100449"},"PeriodicalIF":2.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000190/pdfft?md5=334341ce0f88b6c09ac44ee28059cd03&pid=1-s2.0-S2590037424000190-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140339465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling flow and deformation in porous media from pore-scale to the Darcy-scale","authors":"Zachary Hilliard ,&nbsp;T. Matthew Evans ,&nbsp;Malgorzata Peszynska","doi":"10.1016/j.rinam.2024.100448","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100448","url":null,"abstract":"<div><p>In this paper we address the connections between the computational models of coupled flow and mechanical deformation in soils at the Darcy-scale and pore-scale. At the Darcy scale the Biot model requires data including permeability which is traditionally provided by experiments and empirical measurements. At the pore-scale we consider the Discrete Element Method (DEM) to generate physically realistic assemblies of the particles, and we follow up with the Stokes flow model. Next we apply upscaling to obtain the permeabilities which we find dependent on the deformation. We outline the workflow with its challenges and methods, and present results which show, <em>e.g.</em>, hysteretic dependence of the permeability and porosity on the load. We also show how to incorporate the deformation dependent permeability in a nonlinear Biot model, and illustrate with computational results.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100448"},"PeriodicalIF":2.0,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000189/pdfft?md5=d898a55f18e89b7c4e166ed6d6bd5d46&pid=1-s2.0-S2590037424000189-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140330795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving the general form of the fractional Black–Scholes with two assets through Reconstruction Variational Iteration Method","authors":"Mohammad Hossein Akrami ,&nbsp;Abbas Poya ,&nbsp;Mohammad Ali Zirak","doi":"10.1016/j.rinam.2024.100444","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100444","url":null,"abstract":"<div><p>The objective of this study is to examine the dynamic components of option pricing in the European put option market by utilizing the two-dimensional time fractional-order Black–Scholes equation. To enhance the classical Black–Scholes equation, we utilize the Caputo type of the Katugampola fractional derivative. The Reconstruction of Variational Iteration Method is employed as a powerful tool for analyzing option price behavior in the European-style market. In our investigation, we utilize this method to obtain an exact solution for fractional Black–Scholes with two assets. Moreover, the findings demonstrate the impressive effectiveness of the Reconstruction of Variational Iteration Method in addressing two-dimensional fractional-order differential equations, thereby highlighting its potential as a valuable numerical solution technique.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100444"},"PeriodicalIF":2.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000141/pdfft?md5=4214ce88ab9d4f3ab115e6fb282d676c&pid=1-s2.0-S2590037424000141-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140030118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A truncated matrix variate gamma distribution","authors":"Shokofeh Zinodiny ,&nbsp;Saralees Nadarajah ,&nbsp;Daya K. Nagar","doi":"10.1016/j.rinam.2024.100446","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100446","url":null,"abstract":"<div><p>A truncated form of a matrix variate gamma distribution is introduced and a number of properties of this distribution such as cumulative distribution function, orthogonal invariance, moment generating function, marginal distribution of block matrices, and moments are derived. Some results on distribution of random quadratic forms are also derived.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100446"},"PeriodicalIF":2.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000165/pdfft?md5=98110453a7e2e198d07e4a1f52bb265e&pid=1-s2.0-S2590037424000165-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140030116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Error estimates of characteristic finite elements for bilinear convection–diffusion optimal control problems","authors":"Yuchun Hua,&nbsp;Yuelong Tang","doi":"10.1016/j.rinam.2024.100445","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100445","url":null,"abstract":"<div><p>This paper investigates a fully discrete characteristic finite element approximation of bilinear unsteady convection–diffusion optimal control problems. The characteristic line method is used to treat the convection term and the finite element method is adopted to treat the diffusion term. The state and adjoint state are discretized by piecewise linear functions, the control is approximated by piecewise constant functions. A priori error estimates are derived for the state, adjoint state and control variables. Some numerical examples are provided to confirm our theoretical findings.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"22 ","pages":"Article 100445"},"PeriodicalIF":2.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000153/pdfft?md5=05a003cd457f9c451488ff6f6f452007&pid=1-s2.0-S2590037424000153-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140015389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}