Datasets:
| {"title": "The Boltzmann equation with specular boundary condition in convex\n domains", "year": 2016, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Chanwoo Kim", "Donghyun Lee"], "abstract": " We establish the global-wellposedness and stability of the Boltzmann equation\nwith the specular reflection boundary condition in general smooth convex\ndomains when an initial datum is close to the Maxwellian with or without a\nsmall external potential. In particular, we have completely solved the long\nstanding open problem after an announcement of [20] in 1977.\n", "doi": "10.1002/cpa.21705", "arxiv_id": "1604.04342", "pdf_urls": ["https://arxiv.org/pdf/1604.04342"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics Volume 71 Issue 3\n March 2018 Pages 411-504", "categories": "math.AP"} | |
| {"title": "The SK model is infinite step replica symmetry breaking at zero\n temperature", "year": 2017, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Antonio Auffinger", "Wei-Kuo Chen", "Qiang Zeng"], "abstract": " We prove that the Parisi measure of the mixed p-spin model at zero\ntemperature has infinitely many points in its support. This establishes\nParisi's prediction that the functional order parameter of the\nSherrington-Kirkpatrick model is not a step function at zero temperature. As a\nconsequence, we show that the number of levels of broken replica symmetry in\nthe Parisi formula of the free energy diverges as the temperature goes to zero.\n", "doi": null, "arxiv_id": "1703.06872", "pdf_urls": ["https://arxiv.org/pdf/1703.06872"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "CPAM 2020", "categories": "math.PR math-ph math.MP"} | |
| {"title": "On concavity of the monopolist's problem facing consumers with nonlinear\n price preferences", "year": 2017, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Robert J. McCann", "Kelvin Shuangjian Zhang"], "abstract": " A monopolist wishes to maximize her profits by finding an optimal price\npolicy. After she announces a menu of products and prices, each agent $x$ will\nchoose to buy that product $y(x)$ which maximizes his own utility, if positive.\nThe principal's profits are the sum of the net earnings produced by each\nproduct sold. These are determined by the costs of production and the\ndistribution of products sold, which in turn are based on the distribution of\nanonymous agents and the choices they make in response to the principal's price\nmenu. In this paper, we provide a necessary and sufficient condition for the\nconvexity or concavity of the principal's (bilevel) optimization problem,\nassuming each agent's disutility is a strictly increasing but not necessarily\naffine (i.e. quasilinear) function of the price paid. Concavity when present,\nmakes the problem more amenable to computational and theoretical analysis; it\nis key to obtaining uniqueness and stability results for the principal's\nstrategy in particular. Even in the quasilinear case, our analysis goes beyond\nprevious work by addressing convexity as well as concavity, by establishing\nconditions which are not only sufficient but necessary, and by requiring fewer\nhypotheses on the agents' preferences.\n", "doi": "10.1002/cpa.21817", "arxiv_id": "1709.00632", "pdf_urls": ["https://arxiv.org/pdf/1709.00632"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics 72(7) (2019)\n 1386-1423", "categories": "math.OC math.AP"} | |
| {"title": "Global Identifiability of Differential Models", "year": 2018, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Hoon Hong", "Alexey Ovchinnikov", "Gleb Pogudin", "and Chee Yap"], "abstract": " Many real-world processes and phenomena are modeled using systems of ordinary\ndifferential equations with parameters. Given such a system, we say that a\nparameter is globally identifiable if it can be uniquely recovered from input\nand output data. The main contribution of this paper is to provide theory, an\nalgorithm, and software for deciding global identifiability. First, we\nrigorously derive an algebraic criterion for global identifiability (this is an\nanalytic property), which yields a deterministic algorithm. Second, we improve\nthe efficiency by randomizing the algorithm while guaranteeing the probability\nof correctness. With our new algorithm, we can tackle problems that could not\nbe tackled before. A software based on the algorithm (called SIAN) is available\nat https://github.com/pogudingleb/SIAN.\n", "doi": "10.1002/cpa.21921", "arxiv_id": "1801.08112", "pdf_urls": ["https://arxiv.org/pdf/1801.08112"], "github": ["https://github.com/pogudingleb/SIAN"], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics 73 (2020) 1831-1879", "categories": "math.CA math.AC math.AG math.OC"} | |
| {"title": "Manifolds homotopy equivalent to certain torus bundles over lens spaces", "year": 2019, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["James F. Davis and Wolfgang Lueck"], "abstract": " We compute the topological simple structure set of closed manifolds which\noccur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an\nn-dimensjional torus T^n for an odd prime p and l greater or equal to 3,\nprovided that the induced Z/p-action on pi_1(T^n) = Z^n is free outside the\norigin. To the best of our knowledge this is the first computation of the\nstructure set of a topological manifold whose fundamental group is not obtained\nfrom torsionfree and finite groups using amalgamated and HNN-extensions. We\ngive a collection of classical surgery invariants such as splitting\nobstructions and rho-invariants which decide whether a simple homotopy\nequivalence from a closed topological manifold to M is homotopic to a\nhomeomorphism.\n", "doi": "10.1002/cpa.21941", "arxiv_id": "1907.03345", "pdf_urls": ["https://arxiv.org/pdf/1907.03345"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics, 74 (2021),\n 2348--2397", "categories": "math.GT"} | |
| {"title": "Optimal Small Scale Equidistribution of Lattice Points on the Sphere,\n Heegner Points, and Closed Geodesics", "year": 2019, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Peter Humphries and Maksym Radziwi{\\l}{\\l}"], "abstract": " We asymptotically estimate the variance of the number of lattice points in a\nthin, randomly rotated annulus lying on the surface of the sphere. This\npartially resolves a conjecture of Bourgain, Rudnick, and Sarnak. We also\nobtain estimates that are valid for all balls and annuli that are not too\nsmall. Our results have several consequences: for a conjecture of Linnik on\nsums of two squares and a \"microsquare\", a conjecture of Bourgain and Rudnick\non the number of lattice points lying in small balls on the surface of the\nsphere, the covering radius of the sphere, and the distribution of lattice\npoints in almost all thin regions lying on the surface of the sphere. Finally,\nwe show that for a density $1$ subsequence of squarefree integers, the variance\nexhibits a different asymptotic behaviour for balls of volume $(\\log\nn)^{-\\delta}$ with $0 < \\delta < \\tfrac {1}{16}$.\n We also obtain analogous results for Heegner points and closed geodesics.\nInterestingly, we are able to prove some slightly stronger results for closed\ngeodesics than for Heegner points or lattice points on the surface of the\nsphere. A crucial observation that underpins our proof is the different\nbehaviour of weights functions for annuli and for balls.\n", "doi": "10.1002/cpa.22076", "arxiv_id": "1910.01360", "pdf_urls": ["https://arxiv.org/pdf/1910.01360"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics 75:9 (2022),\n 1936-1996", "categories": "math.NT"} | |
| {"title": "Fast reaction limit with nonmonotone reaction function", "year": 2020, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Beno\\^it Perthame", "Jakub Skrzeczkowski"], "abstract": " We analyse fast reaction limit in the reaction-diffusion system with\nnonmonotone reaction function and one non-diffusing component. As speed of\nreaction tends to infinity, the concentration of non-diffusing component\nexhibits fast oscillations. We identify precisely its Young measure which, as a\nby-product, proves strong convergence of the diffusing component, a result that\nis not obvious from a priori estimates. Our work is based on analysis of\nregularization for forward-backward parabolic equations by Plotnikov. We\nrewrite his ideas in terms of kinetic functions which clarifies the method,\nbrings new insights, relaxes assumptions on model functions and provides a weak\nformulation for the evolution of the Young measure.\n", "doi": null, "arxiv_id": "2008.11086", "pdf_urls": ["https://arxiv.org/pdf/2008.11086"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics, 2022", "categories": "math.AP"} | |
| {"title": "Variational methods for a singular SPDE yielding the universality of the\n magnetization ripple", "year": 2020, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Radu Ignat", "Felix Otto", "Tobias Ried", "Pavlos Tsatsoulis"], "abstract": " The magnetization ripple is a microstructure formed in thin ferromagnetic\nfilms. It can be described by minimizers of a nonconvex energy functional\nleading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by\nwhite noise, which is singular. We address the universal character of the\nmagnetization ripple using variational methods based on $\\Gamma$-convergence.\nDue to the infinite energy of the system, the (random) energy functional has to\nbe renormalized. Using the topology of $\\Gamma$-convergence, we give a sense to\nthe law of the renormalized functional that is independent of the way white\nnoise is approximated. More precisely, this universality holds in the class of\n(not necessarily Gaussian) approximations to white noise satisfying the\nspectral gap inequality, which allows us to obtain sharp stochastic estimates.\nAs a corollary, we obtain the existence of minimizers with optimal regularity.\n", "doi": "10.1002/cpa.22093", "arxiv_id": "2010.13123", "pdf_urls": ["https://arxiv.org/pdf/2010.13123"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics, Volume 76, Issue\n 11, November 2023, Pages 2959-3043", "categories": "math.PR math-ph math.AP math.MP"} | |
| {"title": "Detecting the birth and death of finite-time coherent sets", "year": 2021, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Gary Froyland and P\\'eter Koltai"], "abstract": " Finite-time coherent sets (FTCSs) are distinguished regions of phase space\nthat resist mixing with the surrounding space for some finite period of time;\nphysical manifestations include eddies and vortices in the ocean and\natmosphere, respectively. The boundaries of finite-time coherent sets are\nexamples of Lagrangian coherent structures (LCSs). The selection of the time\nduration over which FTCS and LCS computations are made in practice is crucial\nto their success. If this time is longer than the lifetime of coherence of\nindividual objects then existing methods will fail to detect the shorter-lived\ncoherence. It is of clear practical interest to determine the full lifetime of\ncoherent objects, but in complicated practical situations, for example a field\nof ocean eddies with varying lifetimes, this is impossible with existing\napproaches. Moreover, determining the timing of emergence and destruction of\ncoherent sets is of significant scientific interest. In this work we introduce\nnew constructions to address these issues. The key components are an inflated\ndynamic Laplace operator and the concept of semi-material FTCSs. We make strong\nmathematical connections between the inflated dynamic Laplacian and the\nstandard dynamic Laplacian [Froyland 2015], showing that the latter arises as a\nlimit of the former. The spectrum and eigenfunctions of the inflated dynamic\nLaplacian directly provide information on the number, lifetimes, and evolution\nof coherent~sets.\n", "doi": "10.1002/cpa.22115", "arxiv_id": "2103.16286", "pdf_urls": ["https://arxiv.org/pdf/2103.16286"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics 76(12): 3642--3684,\n 2023", "categories": "math.DS physics.flu-dyn"} | |
| {"title": "Generalization of waving-plate theory to multiple interacting swimmers", "year": 2021, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Peter J. Baddoo", "Nicholas J. Moore", "Anand U. Oza", "Darren G. Crowdy"], "abstract": " Early research in aerodynamics and biological propulsion was dramatically\nadvanced by the analytical solutions of Theodorsen, von K\\'{a}rm\\'{a}n, Wu and\nothers. While these classical solutions apply only to isolated swimmers, the\nflow interactions between multiple swimmers are relevant to many practical\napplications, including the schooling and flocking of animal collectives. In\nthis work, we derive a class of solutions that describe the hydrodynamic\ninteractions between an arbitrary number of swimmers in a two-dimensional\ninviscid fluid. Our approach is rooted in multiply-connected complex analysis\nand exploits several recent results. Specifically, the transcendental\n(Schottky-Klein) prime function serves as the basic building block to construct\nthe appropriate conformal maps and leading-edge-suction functions, which allows\nus to solve the modified Schwarz problem that arises. As such, our solutions\ngeneralize classical thin aerofoil theory, specifically Wu's waving-plate\nanalysis, to the case of multiple swimmers. For the case of a pair of\ninteracting swimmers, we develop an efficient numerical implementation that\nallows rapid computations of the forces on each swimmer. We investigate\nflow-mediated equilibria and find excellent agreement between our new solutions\nand previously reported experimental results. Our solutions recover and unify\ndisparate results in the literature, thereby opening the door for future\nstudies into the interactions between multiple swimmers.\n", "doi": "10.1002/cpa.22113", "arxiv_id": "2106.09167", "pdf_urls": ["https://arxiv.org/pdf/2106.09167"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics, 76(12), 3811-3851\n (2023)", "categories": "physics.flu-dyn math.CV"} | |
| {"title": "Existence of Multi-dimensional Contact Discontinuities for the Ideal\n Compressible Magnetohydrodynamics", "year": 2021, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Yanjin Wang", "Zhouping Xin"], "abstract": " We establish the local existence and uniqueness of multi-dimensional contact\ndiscontinuities for the ideal compressible magnetohydrodynamics (MHD) in\nSobolev spaces, which are most typical interfacial waves for astrophysical\nplasmas and prototypical fundamental waves for hyperbolic systems of\nconservation laws. Such waves are characteristic discontinuities for which\nthere is no flow across the discontinuity surface while the magnetic field\ncrosses transversely, which lead to a two-phase free boundary problem where the\npressure, velocity and magnetic field are continuous across the interface\nwhereas the entropy and density may have jumps. To overcome the difficulties of\npossible nonlinear Rayleigh--Taylor instability and loss of derivatives, here\nwe use crucially the Lagrangian formulation and Cauchy's celebrated integral\n(1815) for the magnetic field. These motivate us to define two special good\nunknowns; one enables us to capture the boundary regularizing effect of the\ntransversal magnetic field on the flow map, and the other one allows us to get\naround the troublesome boundary integrals due to the transversality of the\nmagnetic field. In particular, our result removes the additional assumption of\nthe Rayleigh--Taylor sign condition required by Morando, Trakhinin and\nTrebeschi (\\emph{J. Differential Equations} \\textbf{258} (2015), no. 7,\n2531--2571; \\emph{Arch. Ration. Mech. Anal.} \\textbf{228} (2018), no. 2,\n697--742) and holds for both 2D and 3D and hence gives a complete answer to the\ntwo open questions raised therein. Moreover, there is {\\it no loss of\nderivatives} in our well-posedness theory. The solution is constructed as {\\it\nthe inviscid limit} of solutions to some suitably-chosen nonlinear approximate\nproblems for the two-phase compressible viscous non-resistive MHD.\n", "doi": null, "arxiv_id": "2112.08580", "pdf_urls": ["https://arxiv.org/pdf/2112.08580"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics,77 (2024), no. 1,\n 583--629", "categories": "math.AP math-ph math.MP"} | |
| {"title": "Mean-field limit of non-exchangeable systems", "year": 2021, "venue_abbr": "CPAM", "venue_name": "Communications on Pure and Applied Mathematics", "authors": ["Pierre-Emmanuel Jabin", "David Poyato", "Juan Soler"], "abstract": "This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis but also graph theory through a new concept of limits of sparse graphs (extended graphons) that reflect the structure of the connectivities in the network and has critical effects on the collective dynamics. In this article some of the main restrictive hypothesis in the previous literature on the connectivities between the agents (dense graphs) and the cooperation between them (symmetric interactions) are removed.", "doi": "10.1002/cpa.22235", "arxiv_id": "2112.15406", "pdf_urls": ["https://arxiv.org/pdf/2112.15406"], "github": [], "is_oa": true, "sources": ["open-arxiv"], "type": "journal", "journal_ref": "Communications on Pure and Applied Mathematics, 2024", "categories": "math.PR math.AP"} | |