Journal: SIAM Journal on Applied Mathematics

Abbreviation

SIAM J. Appl. Math.

Publisher

SIAM

Journal Volumes

ISSN

0036-1399
1095-712X

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Publications1 - 10 of 21
  • Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem
    Item type: Journal Article
    Hiptmair, Ralf; Moiola, Andrea; Spence, Euan A. (2022)
    SIAM Journal on Applied Mathematics
    We consider the Helmholtz transmission problem with piecewise-constant material coefficients and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral operators grow rapidly through an increasing sequence of frequencies, even though this is not the case for the solution operator of the transmission problem; we call this phenomenon that of spurious quasi-resonances. We give a rigorous explanation of why and when spurious quasi-resonances occur and propose modified boundary integral equations that are not affected by them.
  • A Mathematical and Numerical Framework for Bubble Meta-Screens
    Item type: Journal Article
    Ammari, Habib; Fitzpatrick, Brian; Gontier, David; et al. (2017)
    SIAM Journal on Applied Mathematics
  • Subwavelength localized modes for acoustic waves in bubbly crystals with a defect
    Item type: Journal Article
    Ammari, Habib; Fitzpatrick, Brian; Orvehed Hiltunen, Erik; et al. (2018)
    SIAM Journal on Applied Mathematics
  • Mathematical modeling in full-field optical coherence elastography
    Item type: Journal Article
    Ammari, Habib; Bretin, Elie; Millien, Pierre; et al. (2015)
    SIAM Journal on Applied Mathematics
  • Mathematical analysis of ultrafast ultrasound imaging
    Item type: Journal Article
    Alberti, Giovanni S.; Ammari, Habib; Romero, Francisco; et al. (2017)
    SIAM Journal on Applied Mathematics
  • On the Validity of the Tight-Binding Method for Describing Systems of Subwavelength Resonators
    Item type: Journal Article
    Ammari, Habib; Fiorani, Francesco; Hiltunen, Erik Orvehed (2022)
    SIAM Journal on Applied Mathematics
    The goal of this paper is to relate the capacitance matrix formalism to the tightbinding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We first study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tight-binding approximation. We prove that the correspondence between the capacitance formulation and the tight-binding approximation holds only in the case of dilute resonators. On the other hand, the tight-binding model is often coupled with a nearest-neighbor approximation, whereby long-range interactions are neglected. Even in the dilute case, we show that long-range interactions between subwavelength resonators are relatively strong and nearest-neighbor approximations are not generally appropriate.
  • Algebraic Study of Receptor-Ligand Systems: A Dose-Response Analysis
    Item type: Journal Article
    Sta, Léa; Adamer, Michael F.; Molina-Paris, Carmen (2024)
    SIAM Journal on Applied Mathematics
    The study of a receptor-ligand system generally relies on the analysis of its dose-response (or concentration-effect) curve, which quantifies the relation between ligand concentration and the biological effect (or cellular response) induced when binding its specific cell surface receptor. Mathematical models of receptor-ligand systems have been developed to compute a dose-response curve under the assumption that the biological effect is proportional to the number of ligand-bound receptors. Given a dose-response curve, two quantities (or metrics) have been defined to characterize the properties of the ligand-receptor system under consideration: amplitude and potency (or half-maximal effective concentration, and denoted by EC₅₀). Both the amplitude and the EC₅₀ are key quantities commonly used in pharmaco-dynamic modeling, yet a comprehensive mathematical investigation of the behavior of these two metrics is still outstanding; for a large (and important) family of receptors, called cytokine receptors, we still do not know how amplitude and EC₅₀ depend on receptor copy numbers. Here we make use of algebraic approaches (Gröbner basis) to study these metrics for a large class of receptor-ligand models, with a focus on cytokine receptors. In particular, we introduce a method, making use of two motivating examples based on the interleukin-7 (IL-7) receptor, to compute analytic expressions for the amplitude and the EC₅₀. We then extend the method to a wider class of receptor-ligand systems, sequential receptor-ligand systems with extrinsic kinase, and provide some examples. The algebraic methods developed in this paper not only reduce computational costs and numerical errors, but allow us to explicitly identify key molecular parameters and rates which determine the behavior of the dose-response curve. Thus, the proposed methods provide a novel and useful approach to perform model validation, assay design and parameter exploration of receptor-ligand systems.
  • Subwavelength Resonances in One-Dimensional High-Contrast Acoustic Media
    Item type: Journal Article
    Feppon, Florian; Cheng, Zijian; Ammari, Habib (2023)
    SIAM Journal on Applied Mathematics
    We propose a mathematical theory of acoustic wave scattering in one-dimensional finite high-contrast media. The system considered is constituted of a finite alternance of high-contrast segments of arbitrary lengths and interdistances, called the “resonators,” and a background medium. We prove the existence of subwavelength resonances, which are the counterparts of the well-known Minnaert resonances in three-dimensional systems. One of the main contribution of the paper is to show that the resonant frequencies as well as the transmission and reflection properties of the system can be accurately predicted by a “capacitance” eigenvalue problem, analogously to the three-dimensional setting. Moreover, we discover new properties which are peculiar to the one-dimensional setting, notably the tridiagonal structure of the capacitance matrix as well as the fact that the first resonant frequency is always exactly zero, implying a low-pass filtering property of a one-dimensional chain of resonators. Numerical results considering different situations with N = 1 to N = 6 resonators are provided to support our mathematical analysis and to illustrate the various possibilities offered by high-contrast resonators to manipulate waves at subwavelength scales.
  • Mathematical modeling of mechanical vibration-assisted conductivity imaging
    Item type: Journal Article
    Ammari, Habib; Lee, Eunjung; Kwon, Hyeuknam; et al. (2015)
    SIAM Journal on Applied Mathematics
  • Lagrangian Transport Through Surfaces in Volume-Preserving Flows
    Item type: Journal Article
    Karrasch, Daniel (2016)
    SIAM Journal on Applied Mathematics
Publications1 - 10 of 21