Pub Date : 2024-09-27DOI: 10.1016/j.amc.2024.129081
Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass.
{"title":"Mass conservation in the validation of fluid-poroelastic structure interaction solvers","authors":"","doi":"10.1016/j.amc.2024.129081","DOIUrl":"10.1016/j.amc.2024.129081","url":null,"abstract":"<div><div>Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-27DOI: 10.1016/j.amc.2024.129075
Rewards, as a form of positive reinforcement, effectively encourage cooperation. In this paper, we study a multi-population prisoner's dilemma game with asymmetric rewards, where agents in the same population play prisoner's dilemma game, and agents from the giver population can reward agents from the recipient population only if they make the same choice. In well-mixed populations, asymmetric rewards can facilitate cooperation. Similarly, asymmetric rewards on the regular square lattice can effectively prevent complete defection. In both well-mixed and structured populations, seemingly disadvantageous cooperative givers play an important role in the maintenance and spread of cooperation. Especially on lattice, cooperative givers with asymmetric rewards can be active in the system through diverse cases of cyclic dominance. Our findings provide deeper insights into the impact of asymmetry on cooperative behavior and the development of altruistic behavior in real-world scenarios.
{"title":"Evolution of cooperation with asymmetric rewards","authors":"","doi":"10.1016/j.amc.2024.129075","DOIUrl":"10.1016/j.amc.2024.129075","url":null,"abstract":"<div><div>Rewards, as a form of positive reinforcement, effectively encourage cooperation. In this paper, we study a multi-population prisoner's dilemma game with asymmetric rewards, where agents in the same population play prisoner's dilemma game, and agents from the giver population can reward agents from the recipient population only if they make the same choice. In well-mixed populations, asymmetric rewards can facilitate cooperation. Similarly, asymmetric rewards on the regular square lattice can effectively prevent complete defection. In both well-mixed and structured populations, seemingly disadvantageous cooperative givers play an important role in the maintenance and spread of cooperation. Especially on lattice, cooperative givers with asymmetric rewards can be active in the system through diverse cases of cyclic dominance. Our findings provide deeper insights into the impact of asymmetry on cooperative behavior and the development of altruistic behavior in real-world scenarios.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-26DOI: 10.1016/j.amc.2024.129078
The availability of digital twins for the cardiovascular system will enable insightful computational tools both for research and clinical practice. This, however, demands robust and well defined models and methods for the different steps involved in the process. We present a vessel coordinate system (VCS) that enables the unambiguous definition of locations in a vessel section, by adapting the idea of cylindrical coordinates to the vessel geometry. Using the VCS model, point correspondence can be defined among different samples of a cohort, allowing data transfer, quantitative comparison, shape coregistration or population analysis. Furthermore, the VCS model allows for the generation of specific meshes (e.g. cylindrical grids, OGrids) necessary for an accurate reconstruction of the geometries used in fluid simulations. We provide the technical details for coordinates computation and discuss the assumptions taken to guarantee that they are well defined. The VCS model is tested in a series of applications. We present a robust, low dimensional, patient specific vascular model and use it to study phenotype variability analysis of the thoracic aorta within a cohort of patients. Point correspondence is exploited to build an haemodynamics atlas of the aorta for the same cohort. The atlas originates from fluid simulations (Navier-Stokes with Finite Volume Method) conducted using OpenFOAMv10. We finally present a relevant discussion on the VCS model, which covers its impact in important areas such as shape modeling and computer fluids dynamics (CFD).
{"title":"A robust shape model for blood vessels analysis","authors":"","doi":"10.1016/j.amc.2024.129078","DOIUrl":"10.1016/j.amc.2024.129078","url":null,"abstract":"<div><div>The availability of digital twins for the cardiovascular system will enable insightful computational tools both for research and clinical practice. This, however, demands robust and well defined models and methods for the different steps involved in the process. We present a vessel coordinate system (VCS) that enables the unambiguous definition of locations in a vessel section, by adapting the idea of cylindrical coordinates to the vessel geometry. Using the VCS model, point correspondence can be defined among different samples of a cohort, allowing data transfer, quantitative comparison, shape coregistration or population analysis. Furthermore, the VCS model allows for the generation of specific meshes (e.g. cylindrical grids, OGrids) necessary for an accurate reconstruction of the geometries used in fluid simulations. We provide the technical details for coordinates computation and discuss the assumptions taken to guarantee that they are well defined. The VCS model is tested in a series of applications. We present a robust, low dimensional, patient specific vascular model and use it to study phenotype variability analysis of the thoracic aorta within a cohort of patients. Point correspondence is exploited to build an haemodynamics atlas of the aorta for the same cohort. The atlas originates from fluid simulations (Navier-Stokes with Finite Volume Method) conducted using OpenFOAMv10. We finally present a relevant discussion on the VCS model, which covers its impact in important areas such as shape modeling and computer fluids dynamics (CFD).</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-26DOI: 10.1016/j.amc.2024.129080
Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often incur significant computational costs. This paper introduces an efficient application of a Legendre-Laguerre basis for absorbing layers for two-dimensional non-linear compressible Euler equations. The method couples a spectral-element bounded domain with a semi-infinite region, employing a tensor product of Lagrange and scaled Laguerre basis functions. Semi-infinite elements are used in the absorbing layer with Rayleigh damping. In comparison to existing methods with similar absorbing layer extensions, this approach, a pioneering application to the Euler equations of compressible and stratified flows, demonstrates substantial computational savings. The study marks the first application of semi-infinite elements to mitigate wave reflection in the solution of the Euler equations, particularly in nonhydrostatic atmospheric modeling. A comprehensive set of tests demonstrates the method's versatility for general systems of conservation laws, with a focus on its effectiveness in damping vertically propagating mountain gravity waves, a benchmark for atmospheric models. Across all tests, the model presented in this paper consistently exhibits notable performance improvements compared to a traditional Rayleigh damping approach.
{"title":"Efficient spectral element method for the Euler equations on unbounded domains","authors":"","doi":"10.1016/j.amc.2024.129080","DOIUrl":"10.1016/j.amc.2024.129080","url":null,"abstract":"<div><div>Mitigating the impact of waves leaving a numerical domain has been a persistent challenge in numerical modeling. Reducing wave reflection at the domain boundary is crucial for accurate simulations. Absorbing layers, while common, often incur significant computational costs. This paper introduces an efficient application of a Legendre-Laguerre basis for absorbing layers for two-dimensional non-linear compressible Euler equations. The method couples a spectral-element bounded domain with a semi-infinite region, employing a tensor product of Lagrange and scaled Laguerre basis functions. Semi-infinite elements are used in the absorbing layer with Rayleigh damping. In comparison to existing methods with similar absorbing layer extensions, this approach, a pioneering application to the Euler equations of compressible and stratified flows, demonstrates substantial computational savings. The study marks the first application of semi-infinite elements to mitigate wave reflection in the solution of the Euler equations, particularly in nonhydrostatic atmospheric modeling. A comprehensive set of tests demonstrates the method's versatility for general systems of conservation laws, with a focus on its effectiveness in damping vertically propagating mountain gravity waves, a benchmark for atmospheric models. Across all tests, the model presented in this paper consistently exhibits notable performance improvements compared to a traditional Rayleigh damping approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.amc.2024.129076
<div><div>Introducing adaptation parameters <span><math><mi>σ</mi><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, formal parameters <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>,</mo><mi>κ</mi><mo>,</mo><mi>τ</mi></math></span>, and type parameters <span><math><mi>μ</mi><mo>,</mo><mi>ν</mi></math></span>, the integration operator is defined as <span><math><mi>T</mi><mo>:</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>μ</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo><mo>→</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mi>ν</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></math></span>, <span><math><mi>T</mi><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub><mfrac><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>κ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>τ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>d</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. Using the weight function method, a general Hilbert-type integral inequality is obtained, thereby proving the boundedness of the operator. The constant factor of the general Hilbert-type inequality is the best possible if and only if the adaptation parameters satisfy <span><math><mi>σ</mi><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. From this, the formula for calculating the operator norm is obtained. In terms of application, some results from the references have been
{"title":"The equivalent conditions for norm of a Hilbert-type integral operator with a combination kernel and its applications","authors":"","doi":"10.1016/j.amc.2024.129076","DOIUrl":"10.1016/j.amc.2024.129076","url":null,"abstract":"<div><div>Introducing adaptation parameters <span><math><mi>σ</mi><mo>,</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, formal parameters <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>,</mo><mi>κ</mi><mo>,</mo><mi>τ</mi></math></span>, and type parameters <span><math><mi>μ</mi><mo>,</mo><mi>ν</mi></math></span>, the integration operator is defined as <span><math><mi>T</mi><mo>:</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>μ</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo><mo>→</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mi>ν</mi><mover><mrow><mi>σ</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></math></span>, <span><math><mi>T</mi><mi>f</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></mrow></msub><mfrac><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>κ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup><mo>+</mo><mi>τ</mi><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><msup><mrow><mi>x</mi></mrow><mrow><mi>μ</mi></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi></mrow></msup></mrow></msup></mrow></mfrac><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>d</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>. Using the weight function method, a general Hilbert-type integral inequality is obtained, thereby proving the boundedness of the operator. The constant factor of the general Hilbert-type inequality is the best possible if and only if the adaptation parameters satisfy <span><math><mi>σ</mi><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. From this, the formula for calculating the operator norm is obtained. In terms of application, some results from the references have been ","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.amc.2024.129074
<div><div>A signed total Roman dominating function (STRDF) on a graph <em>G</em> is a function <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⟶</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span> satisfying (i) <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>x</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>1</mn></math></span> for each vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and its neighborhood <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <em>G</em> and, (ii) every vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mo>−</mo><mn>1</mn></math></span>, there exists a vertex <span><math><mi>v</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></math></span>. The minimum number <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> among all STRDFs <em>f</em> on <em>G</em> is denoted by <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. A set <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>}</mo></math></span> of distinct STRDFs on <em>G</em> is called a signed total Roman dominating family on <em>G</em> if <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span> for each <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. We use <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to denote the maximum number of functions among all signed total Roman dominating families on <em>G</em>. Our purpose in this paper is to examine the effects on <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> when <em>G</em> is modified by removing or subdividing an edge. In addition, we determine the number <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for the case that <em>G</em> is a complete g
图 G 上的有符号总罗马占优函数 (STRDF) 是一个函数 f：V(G)⟶{-1,1,2}，满足：(i) 对于 G 中的每个顶点 ux∈V(G) 及其邻域 NG(u)，∑x∈NG(u)f(x)≥1；(ii) f(u)=-1 的每个顶点 u∈V(G)，都存在 f(v)=2 的顶点 v∈NG(u)。在 G 上的所有 STRDF f 中，∑u∈V(G)f(u) 的最小数目用 γstR(G) 表示。如果对于每个 u∈V(G)，∑i=1dfi(u)≤1，则 G 上不同 STRDF 的集合 {f1,...,fd}称为 G 上的有符号总罗马支配族。我们用 dstR(G) 表示 G 上所有有符号罗马支配族中函数的最大数目。本文的目的是研究当通过删除或细分一条边来修改 G 时对γstR(G) 的影响。此外，我们还确定了 G 是完整图或二叉图时的 dstR(G) 数。
{"title":"Signed total Roman domination and domatic numbers in graphs","authors":"","doi":"10.1016/j.amc.2024.129074","DOIUrl":"10.1016/j.amc.2024.129074","url":null,"abstract":"<div><div>A signed total Roman dominating function (STRDF) on a graph <em>G</em> is a function <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>⟶</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></span> satisfying (i) <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>x</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mn>1</mn></math></span> for each vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and its neighborhood <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> in <em>G</em> and, (ii) every vertex <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mo>−</mo><mn>1</mn></math></span>, there exists a vertex <span><math><mi>v</mi><mo>∈</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo></math></span> with <span><math><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></math></span>. The minimum number <span><math><msub><mrow><mo>∑</mo></mrow><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> among all STRDFs <em>f</em> on <em>G</em> is denoted by <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. A set <span><math><mo>{</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>}</mo></math></span> of distinct STRDFs on <em>G</em> is called a signed total Roman dominating family on <em>G</em> if <span><math><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></msubsup><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span> for each <span><math><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. We use <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to denote the maximum number of functions among all signed total Roman dominating families on <em>G</em>. Our purpose in this paper is to examine the effects on <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> when <em>G</em> is modified by removing or subdividing an edge. In addition, we determine the number <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>t</mi><mi>R</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for the case that <em>G</em> is a complete g","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-16DOI: 10.1016/j.amc.2024.129070
In this paper, the issue of event-triggered fixed-time tracking control is investigated for a class of nonlinear systems subject to unknown control directions (UCDs) and asymmetric input saturation. Firstly, to cope with the design challenge imposed by nondifferential saturation nonlinearity in the system, the asymmetric saturation function is approached by introducing a smooth nonlinear function with respect to the control input signal. Secondly, a variable separation technique lemma is developed to remove the restrictive growth conditions that must be fulfilled by the nonlinear functions, and a new practically fixed-time stability lemma with more accurate upper-bound estimate of the settling time is put forward by means of the Beta function. Then, a technical lemma regarding a class of type-B Nussbaum functions (NFs) with unique properties is introduced, which avoids specific NFs-based complex stability analysis. Moreover, in compensation for the sampling error incurred by the event-triggered mechanism under UCDs, an adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. The results show that the controlled system is practically fixed-time stable (PFxTS), the tracking error can converge to a small neighborhood of the origin in a fixed time, and the saturation constraint is satisfied while reducing the communication burden. Finally, the effectiveness of the practically fixed-time stability criterion and control method developed in this study are verified by two simulation examples.
本文针对一类存在未知控制方向（UCD）和非对称输入饱和的非线性系统，研究了事件触发固定时间跟踪控制问题。首先，为了应对系统中的非差分饱和非线性所带来的设计挑战，通过引入与控制输入信号有关的平滑非线性函数来处理非对称饱和函数。其次，建立了一个变量分离技术两用例，以消除非线性函数必须满足的限制性增长条件，并通过 Beta 函数提出了一个新的实际固定时间稳定性两用例，该两用例具有更精确的沉降时间上限估计。然后，引入了关于一类具有独特性质的 B 型努斯鲍姆函数（NFs）的技术公 式，从而避免了基于 NFs 的特定复杂稳定性分析。此外，为补偿事件触发机制在 UCDs 下产生的采样误差，巧妙地构建了自适应法则，以共同设计固定时间控制法则和事件触发机制。结果表明，受控系统实际上是固定时间稳定（PFxTS）的，跟踪误差可以在固定时间内收敛到原点的一个小邻域，并且在减少通信负担的同时满足了饱和约束。最后，本研究开发的实际固定时间稳定性准则和控制方法的有效性通过两个仿真实例得到了验证。
{"title":"Event-triggered sampling-based singularity-free fixed-time control for nonlinear systems subject to input saturation and unknown control directions","authors":"","doi":"10.1016/j.amc.2024.129070","DOIUrl":"10.1016/j.amc.2024.129070","url":null,"abstract":"<div><p>In this paper, the issue of event-triggered fixed-time tracking control is investigated for a class of nonlinear systems subject to unknown control directions (UCDs) and asymmetric input saturation. Firstly, to cope with the design challenge imposed by nondifferential saturation nonlinearity in the system, the asymmetric saturation function is approached by introducing a smooth nonlinear function with respect to the control input signal. Secondly, a variable separation technique lemma is developed to remove the restrictive growth conditions that must be fulfilled by the nonlinear functions, and a new practically fixed-time stability lemma with more accurate upper-bound estimate of the settling time is put forward by means of the Beta function. Then, a technical lemma regarding a class of type-B Nussbaum functions (NFs) with unique properties is introduced, which avoids specific NFs-based complex stability analysis. Moreover, in compensation for the sampling error incurred by the event-triggered mechanism under UCDs, an adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. The results show that the controlled system is practically fixed-time stable (PFxTS), the tracking error can converge to a small neighborhood of the origin in a fixed time, and the saturation constraint is satisfied while reducing the communication burden. Finally, the effectiveness of the practically fixed-time stability criterion and control method developed in this study are verified by two simulation examples.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-16DOI: 10.1016/j.amc.2024.129072
This note aims to manifest the existence of a class of α-fractal interpolation functions (α-FIFs) without boundary point conditions at the m-th level in the space consisting of continuous functions on the Sierpiński gasket (SG). Furthermore, we add the existence of the same class in the space and energy space on SG. Under certain hypotheses, we show the existence of α-FIFs without boundary point conditions in the Hölder space and oscillation space on SG, and also calculate the fractal dimensions of their graphs.
{"title":"Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket","authors":"","doi":"10.1016/j.amc.2024.129072","DOIUrl":"10.1016/j.amc.2024.129072","url":null,"abstract":"<div><p>This note aims to manifest the existence of a class of <em>α</em>-fractal interpolation functions (<em>α</em>-FIFs) without boundary point conditions at the <em>m</em>-th level in the space consisting of continuous functions on the Sierpiński gasket (<em>SG</em>). Furthermore, we add the existence of the same class in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> space and energy space on <em>SG</em>. Under certain hypotheses, we show the existence of <em>α</em>-FIFs without boundary point conditions in the Hölder space and oscillation space on <em>SG</em>, and also calculate the fractal dimensions of their graphs.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142238254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-13DOI: 10.1016/j.amc.2024.129058
In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular p-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.
{"title":"Efficient finite element strategy using enhanced high-order and second-derivative-free variants of Newton's method","authors":"","doi":"10.1016/j.amc.2024.129058","DOIUrl":"10.1016/j.amc.2024.129058","url":null,"abstract":"<div><p>In this work, we propose a stable finite element approximation by extending higher-order Newton's method to the multidimensional case for solving nonlinear systems of partial differential equations. This approach relies solely on the evaluation of Jacobian matrices and residuals, eliminating the need for computing higher-order derivatives. Achieving third and fifth-order convergence, it ensures stability and allows for significantly larger time steps compared to explicit methods. We thoroughly address accuracy and convergence, focusing on the singular <em>p</em>-Laplacian problem and the time-dependent lid-driven cavity benchmark. A globalized variant incorporating a continuation technique is employed to effectively handle high Reynolds number regimes. Through two-dimensional and three-dimensional numerical experiments, we demonstrate that the improved cubically convergent variant outperforms others, leading to substantial computational savings, notably halving the computational cost for the lid-driven cavity test at large Reynolds numbers.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1016/j.amc.2024.129005
This paper considers a biological model in which two stages of the population, adults and preadults, are modeled by a Beverton-Holt type function and a logistic-type function. Two new models are proposed, each with an additional parameter representing the compensation. This new parameter is introduced in adult and juvenile populations. As a result, the Allee effect is observed in both models. The scenario of almost sure extinction can appear when the dynamic is chaotic enough.
{"title":"On the dynamics of a linear-hyperbolic population model with Allee effect and almost sure extinction","authors":"","doi":"10.1016/j.amc.2024.129005","DOIUrl":"10.1016/j.amc.2024.129005","url":null,"abstract":"<div><p>This paper considers a biological model in which two stages of the population, adults and preadults, are modeled by a Beverton-Holt type function and a logistic-type function. Two new models are proposed, each with an additional parameter representing the compensation. This new parameter is introduced in adult and juvenile populations. As a result, the Allee effect is observed in both models. The scenario of almost sure extinction can appear when the dynamic is chaotic enough.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142173692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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