Mathematical Models and Methods in Applied Sciences最新文献

{"title":"Kinetic theory of active particles meets auction theory","authors":"Carla Crucianelli, Juan Pablo Pinasco, Nicolas Saintier","doi":"10.1142/s0218202524400086","DOIUrl":"https://doi.org/10.1142/s0218202524400086","url":null,"abstract":"<p>In this paper we study Nash equilibria in auctions from the kinetic theory of active particles point of view. We propose a simple learning rule for agents to update their bidding strategies based on their previous successes and failures, in first-price auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of agents on the bidding strategies. We show that the stationary solution of the equation corresponds to the symmetric Nash equilibrium of the auction, and we prove the convergence to this stationary solution when time goes to infinity. We also introduce a more general learning rule that only depends on the income of agents, and we apply to both first- and second-price auctions. We show that agents learn the Nash equilibrium in first- and second-price auctions with these rules. We present agent-based simulations of the models, and we discuss several open problems.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers","authors":"Giuseppe Cardone, Willi Jager, J. L. Woukeng","doi":"10.1142/s0218202524500246","DOIUrl":"https://doi.org/10.1142/s0218202524500246","url":null,"abstract":"We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele-Shaw equation with memory coupled with the convective Cahn-Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"21 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Particle Paths of Hyperbolic Conservation Laws","authors":"U. S. Fjordholm, Ola I. H. Maehlen, Magnus C. Orke","doi":"10.1142/s0218202524500209","DOIUrl":"https://doi.org/10.1142/s0218202524500209","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"29 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity","authors":"Weizhu Bao, Ying Ma, Chushan Wang","doi":"10.1142/s0218202524500155","DOIUrl":"https://doi.org/10.1142/s0218202524500155","url":null,"abstract":"<p>We establish optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and typical power-type nonlinearity <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi><mo stretchy=\"false\">(</mo><mi>ρ</mi><mo stretchy=\"false\">)</mo><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>σ</mi></mrow></msup></math></span><span></span>, where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ρ</mi><mo>:</mo><mo>=</mo><mo>|</mo><mi>ψ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span> is the density with <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>ψ</mi></math></span><span></span> the wave function and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span> the exponent of the nonlinearity. For the first-order Lie–Trotter time-splitting method, optimal <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-norm error bound is proved for <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span>, and optimal <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-norm error bound is obtained for <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>≥</mo><mn>1</mn><mo stretchy=\"false\">/</mo><mn>2</mn></math></span><span></span>. For the second-order Strang time-splitting method, optimal <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-norm error bound is established for <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>≥</mo><mn>1</mn></math></span><span></span>, and optimal <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-norm error bound is proved for <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00016.gif\" display","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Kinetic compartmental models driven by opinion dynamics: Vaccine hesitancy and social influence","authors":"Andrea Bondesan, Giuseppe Toscani, Mattia Zanella","doi":"10.1142/s0218202524400062","DOIUrl":"https://doi.org/10.1142/s0218202524400062","url":null,"abstract":"<p>We propose a kinetic model for understanding the link between opinion formation phenomena and epidemic dynamics. The recent pandemic has brought to light that vaccine hesitancy can present different phases and temporal and spatial variations, presumably due to the different social features of individuals. The emergence of patterns in societal reactions permits to design and predict the trends of a pandemic. This suggests that the problem of vaccine hesitancy can be described in mathematical terms, by suitably coupling a kinetic compartmental model for the spreading of an infectious disease with the evolution of the personal opinion of individuals, in the presence of leaders. The resulting model makes it possible to predict the collective compliance with vaccination campaigns as the pandemic evolves and to highlight the best strategy to set up for maximizing the vaccination coverage. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entropy-based convergence rates of greedy algorithms","authors":"Yuwen Li, Jonathan W. Siegel","doi":"10.1142/s0218202524500143","DOIUrl":"https://doi.org/10.1142/s0218202524500143","url":null,"abstract":"<p>We present convergence estimates of two types of greedy algorithms in terms of the entropy numbers of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the entropy numbers of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-widths and enables us to obtain direct comparisons between the algorithm error and the entropy numbers, where the multiplicative constants are explicit and simple. The entropy-based convergence estimate is sharp and improves upon the classical width-based analysis of reduced basis methods for elliptic model problems. In the second part, we derive a novel and simple convergence analysis of the classical orthogonal greedy algorithm for nonlinear dictionary approximation using the entropy numbers of the symmetric convex hull of the dictionary. This also improves upon existing results by giving a direct comparison between the algorithm error and the entropy numbers.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"135 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A particle method for non-local advection–selection–mutation equations","authors":"Frank Ernesto Alvarez, Jules Guilberteau","doi":"10.1142/s0218202524500106","DOIUrl":"https://doi.org/10.1142/s0218202524500106","url":null,"abstract":"<p>The well-posedness of a non-local advection–selection–mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularized sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite interval is shown and an explicit rate of convergence is given. Furthermore, we investigate the asymptotic-preserving properties of the method in large times, providing sufficient conditions for it to hold true as well as examples and counter-examples. Finally, we illustrate the method in two cases taken from the literature.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Derivation of effective theories for thin 3D nonlinearly elastic rods with voids","authors":"Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas","doi":"10.1142/s0218202524500131","DOIUrl":"https://doi.org/10.1142/s0218202524500131","url":null,"abstract":"<p>We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>-convergence. Hereby, we generalize the results of the purely elastic setting [M. G. Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>-convergence, <i>Calc. Var. Partial Differential Equations</i><b>18</b> (2003) 287–305] to a framework of free discontinuity problems. The effective one-dimensional model features a classical elastic bending–torsion energy, but also accounts for the possibility that the limiting rod can be broken apart into several pieces or folded. The latter phenomenon can occur because of the persistence of voids in the limit, or due to their collapsing into a discontinuity of the limiting deformation or its derivative. The main ingredient in the proof is a novel rigidity estimate in varying domains under vanishing curvature regularization, obtained in [M. Friedrich, L. Kreutz and K. Zemas, Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces, preprint (2021), arXiv:2107.10808].</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Impact of a unilateral horizontal gene transfer on the evolutionary equilibria of a population","authors":"Alejandro Gárriz, Alexis Leculier, S. Mirrahimi","doi":"10.1142/s0218202524500192","DOIUrl":"https://doi.org/10.1142/s0218202524500192","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inf-sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment","authors":"Volker John, Xu Li, Christian Merdon, Hongxing Rui","doi":"10.1142/s0218202524500180","DOIUrl":"https://doi.org/10.1142/s0218202524500180","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"3 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}