{"title":"Analysis of Gaussian vs. Triangular Profiles for traffic flow modeling","authors":"Ghada A. Ahmed, Reem Algethamie","doi":"10.1016/j.rinam.2025.100555","DOIUrl":"10.1016/j.rinam.2025.100555","url":null,"abstract":"<div><div>The present work provides a comprehensive comparative analysis between two advanced traffic density profiles — the Enhanced Gaussian Profile with Dynamic skewness and sigmoidal Spread, and the Novel Modified Triangular Profile with Interacting Peaks and Adaptive Heights — within the framework of the fractional Lighthill–Whitham–Richards (FLWR), which is an extension of the classical LWR model (Lighthill and Whitham, 1955; Richards, 1956; Sun and Zhang, 2011). The improved Gaussian Profile includes time-dependent skewness and spread, allowing it to dynamically adapt to changes in traffic conditions. On the other hand, the Modified Triangular Profile represents complex interactions between several congestion peaks (Newell, 1993; Treiber et al., 2000), similar to the multi-peak congestion phenomenon (Helbing, 2001; Kerner, 2004). The Von Neumann Stability Analysis (von Neumann and Richtmyer, 1950; von Neumann and Richtmyer, 1947) is employed and applied to both profiles to assess their stability under various traffic scenarios, providing valuable insights into the conditions under which each model remains robust.</div><div>We conducted a comparison between simulated traffic density data and real-world measurements to evaluate the accuracy and applicability of each profile. Our findings reveal a significant disparity in how these profiles capture small differences in traffic flow, particularly in situations that involve sudden changes in traffic patterns or external factors like weather conditions. This study not only enhances our understanding of traffic density modeling but also offers a framework for selecting acceptable traffic profiles based on specific real-world scenarios. The findings are essential for enhancing traffic management systems and designing more effective road networks (Richards, 1956; Mainardi, 2010; van der Houwen and Gijzen, 2010).</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100555"},"PeriodicalIF":1.4,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143577569","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":"Wallach’s ratio principle under affine representation","authors":"Eszter Gselmann","doi":"10.1016/j.rinam.2025.100554","DOIUrl":"10.1016/j.rinam.2025.100554","url":null,"abstract":"<div><div>Motivated by Heller (2014) and supplementing the results found there, the main objective of this paper is to study the near-miss to Wallach’s ratio principle and the near-miss to illumination invariance, assuming more general psychophysical representations than in the previous works. We employ a model-creation technique founded on functional equations to study the affine and gain-control type representations of these phenomena, respectively.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100554"},"PeriodicalIF":1.4,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563338","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 of positive solutions for classes of Laplacian systems with sign change weight functions and nonlinear boundary conditions","authors":"A. Shabanpour, S.H. Rasouli","doi":"10.1016/j.rinam.2024.100525","DOIUrl":"10.1016/j.rinam.2024.100525","url":null,"abstract":"<div><div>We establish some results for positive solutions to class of Laplacian systems with positive parameter, sign change weight functions and nonlinear boundary conditions, in particular, we discuss the existence of positive solutions for a certain range of our parameter using the method of sub-super solutions. Additionally, we introduce novel conditions to ensure the existence of positive solutions for the given system.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100525"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098470","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}
Sanna Mönkölä, Jukka Räbinä, Tytti Saksa, Tuomo Rossi
{"title":"(2+1)-dimensional discrete exterior discretization of a general wave model in Minkowski spacetime","authors":"Sanna Mönkölä, Jukka Räbinä, Tytti Saksa, Tuomo Rossi","doi":"10.1016/j.rinam.2024.100528","DOIUrl":"10.1016/j.rinam.2024.100528","url":null,"abstract":"<div><div>We present a differential geometry-based model for linear wave equations in <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional spacetime. This model encompasses acoustic, elastic, and electromagnetic waves and is also applicable in quantum mechanical simulations. For discretization, we introduce a spacetime extension of discrete exterior calculus, resulting in a leapfrog-style time evolution. The scheme further supports numerical simulations of moving and deforming domains. The numerical tests presented in this paper demonstrate the method’s stability limits and computational efficiency.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100528"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098511","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":"Blow-up Whitney forms, shadow forms, and Poisson processes","authors":"Yakov Berchenko-Kogan , Evan S. Gawlik","doi":"10.1016/j.rinam.2024.100529","DOIUrl":"10.1016/j.rinam.2024.100529","url":null,"abstract":"<div><div>The Whitney forms on a simplex <span><math><mi>T</mi></math></span> admit high-order generalizations that have received a great deal of attention in numerical analysis. Less well-known are the <em>shadow forms</em> of Brasselet, Goresky, and MacPherson. These forms generalize the Whitney forms, but have rational coefficients, allowing singularities near the faces of <span><math><mi>T</mi></math></span>. Motivated by numerical problems that exhibit these kinds of singularities, we introduce degrees of freedom for the shadow <span><math><mi>k</mi></math></span>-forms that are well-suited for finite element implementations. In particular, we show that the degrees of freedom for the shadow forms are given by integration over the <span><math><mi>k</mi></math></span>-dimensional faces of the <em>blow-up</em> <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span> of the simplex <span><math><mi>T</mi></math></span>. Consequently, we obtain an isomorphism between the cohomology of the complex of shadow forms and the cellular cohomology of <span><math><mover><mrow><mi>T</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>, which vanishes except in degree zero. Additionally, we discover a surprising probabilistic interpretation of shadow forms in terms of Poisson processes. This perspective simplifies several proofs and gives a way of computing bases for the shadow forms using a straightforward combinatorial calculation.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100529"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098512","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}
Lionel Ouya Ndjansi, Laurent Tchoualag, Jean Louis Woukeng
{"title":"Efficient numerical methods to approach solutions of quasi-static contact problems","authors":"Lionel Ouya Ndjansi, Laurent Tchoualag, Jean Louis Woukeng","doi":"10.1016/j.rinam.2024.100535","DOIUrl":"10.1016/j.rinam.2024.100535","url":null,"abstract":"<div><div>In this paper, a new boundary element method and generalized Newton method for the resolution of quasi-static contact problems with friction in 2D is presented. The time discretization of the model and the mixed duality-fixed point formulation combined with augmented lagrangian approach are considered. This leads at each time step, to a system of static contact problem with Coulomb friction, where the study is carried out by the dual–primal active set method. After proving the well-posedness of the regularized dual problem and convergence to the solutions of the static problem, the generalized Newton method based on active set strategy method and fixed point method are constructed. An error estimate for the Galerkin discretization is established and some numerical examples are presented.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100535"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098510","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":"Stochastic differential equations harvesting optimization with stochastic prices: Formulation and numerical solution","authors":"Miguel Reis, Nuno M. Brites","doi":"10.1016/j.rinam.2024.100533","DOIUrl":"10.1016/j.rinam.2024.100533","url":null,"abstract":"<div><div>This work aims to achieve optimal harvesting in a random setting with a stochastic price structure. We use a general growth function to model the harvested population, a geometric Brownian motion to model price change, and add fluctuations in the interest rate over time to complete the analysis. Following this, we make use of the stochastic dynamic programming technique in order to obtain the Hamilton–Jacobi–Bellman equation, which ultimately results in the optimal combination of profit and effort. We employ the Crank–Nicolson discretization approach to obtain a numerical solution to the Hamilton–Jacobi–Bellman partial differential equation. For application purposes, we consider a Gompertz growth model and realistic data based on the Bangladesh shrimp.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100533"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150063","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 finite element/polynomial spectral mixed approximation for the Stokes problem","authors":"Shinya Uchiumi","doi":"10.1016/j.rinam.2025.100550","DOIUrl":"10.1016/j.rinam.2025.100550","url":null,"abstract":"<div><div>A mixed Galerkin approximation for the Stokes problem is proposed. The finite element approximation is used for the velocity and the polynomial spectral approximation for pressure. The numerical results show that the proposed method has higher accuracy for a problem with a large external force, and efficiency in solving the resultant linear system using an iterative solver.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100550"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487225","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":"Kolmogorov bounds for drift parameter estimation of continuously-observed SPDEs","authors":"Fares Alazemi, Abdulaziz Alsenafi, Khalifa Es-Sebaiy","doi":"10.1016/j.rinam.2025.100538","DOIUrl":"10.1016/j.rinam.2025.100538","url":null,"abstract":"<div><div>The purpose of this paper is to study the asymptotic behavior of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) of the drift coefficient for a stochastic partial differential equation based on continuous time observations of the Fourier coefficients <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>N</mi></mrow></math></span> of the solution, over some finite interval of time <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></math></span>. More precisely, we derive Berry–Esseen bounds in Kolmogorov distance for the MLE and MCE when <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> and/or <span><math><mrow><mi>T</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. Moreover, we prove the strong consistency of the MCE as <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> and/or <span><math><mrow><mi>T</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100538"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149996","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 novel n-L1 image restoration approach","authors":"Lufeng Bai","doi":"10.1016/j.rinam.2024.100521","DOIUrl":"10.1016/j.rinam.2024.100521","url":null,"abstract":"<div><div>This article presents a variational image restoration model and an accelerated algorithm to recover a clear image from a noisy and blurred version. The model involves solving a high-order nonlinear partial differential equation, which can be computationally expensive. This paper proposes the use of the accelerated alternating direction method of multipliers (ADMM) to solve a constrained minimization problem. The method is based on a variable splitting scheme and an augmented Lagrangian method, resulting in a fast and convergent algorithm. The paper presents a convergence analysis of the proposed algorithm under certain conditions. Numerical results and comparisons demonstrate that our model and algorithm outperform some state-of-the-art algorithms for image restoration in terms of computational time.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100521"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098503","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}