Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Abbreviation

Proc. R. Soc. A.

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Royal Society

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ISSN

1471-2946

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Publications1 - 10 of 81
  • The mechanism of delayed release in earthquake-induced avalanches
    Item type: Journal Article
    Puzrin, Alexander M.; Faug, Thierry; Einav, Itai (2019)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Snow avalanches can be triggered by strong earthquakes. Most existing models assume that snow slab avalanches happen simultaneously during or immediately after their triggering. Therefore, they cannot explain the plausibility of delayed avalanches that are released minutes to hours after a quake. This paper establishes the basic mechanism of delays in earthquake-induced avalanche release using a novel analytical model that yields dynamics consistent with three documented cases, including two from Western Himalaya and one from central Italy. The mechanism arises from the interplay between creep, strain softening and strain-rate sensitivity of snow, which drive the growth of a basal shear fracture. Our model demonstrates that earthquake-triggered delayed avalanches are rare, yet possible, and could lead to significant damage, especially in long milder slopes. The generality of the model formulation opens a new approach for exploring many other problems related to natural slab avalanche release.
  • Optimizing information transmission rates drives brain gyrification
    Item type: Journal Article
    Heyden, Stefanie; Ortiz, Michael (2018)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    We investigate the functional optimality of the cerebral cortex of an adult human brain geometry. Unlike most competing models, we postulate that the cerebral cortex formation is driven by the objective of maximizing the total information transmission rate. Starting from a random path model, we show that this optimization problem is related to the Steklov eigenvalue problem. Combining realistic brain geometries with the finite-element method, we calculate the underlying Steklov eigenvalues and eigenfunctions. By comparison to a convex hull approximation, we show that the adult human brain geometry indeed reduces the Steklov eigenvalue spectrum and thus increases the rate at which information is exchanged between points on the cerebral cortex. With a view to possible clinical applications, the leading Steklov eigenfunctions and the resulting induced magnetic fields are computed and reported.
  • A high-resolution discourse on seismic tomography
    Item type: Journal Article
    Fichtner, Andreas; Ritsema, Jeroen; Thrastarson, Sölvi (2025)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Advances in data acquisition and numerical wave simulation have improved tomographic imaging techniques and results, but actual users of tomographic models may find it difficult to understand which model is best for their needs. This article is intended for these users. We argue that our notion of best is influenced by the extent to which models satisfy our biases. We explain how the basic types of seismic waves see the Earth structure, illustrate the essential strategy of seismic tomography, discuss advanced adaptations such as full-waveform inversion (FWI) and emphasize the artistic components of tomography. The compounding effect of a plethora of reasonable, yet subjective choices is a range of models that differ more than their individual uncertainty analyses may suggest. Perhaps counter-intuitively, we argue producing similar tomographic models should not be the goal of seismic tomography. Instead, we promote a Community Monte Carlo effort to assemble a range of dissimilar models based on different modelling approaches and subjective choices, but which explain the seismic data. This effort could serve as input for geodynamic inferences with meaningful seismic uncertainties.
  • How do conservative backbone curves perturb into forced responses? A Melnikov function analysis
    Item type: Journal Article
    Cenedese, Mattia; Haller, George (2020)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems
    Item type: Journal Article
    Breunung, Thomas; Haller, George (2018)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • Unidirectional edge modes in time-modulated metamaterials
    Item type: Journal Article
    Ammari, Habib; Cao, Jinghao (2022)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponding to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-modulation amplitude are illustrated by several numerical simulations.
  • Inertial modes in a rotating triaxial ellipsoid
    Item type: Journal Article
    Vantieghem, Stijn (2014)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whether any arbitrary velocity field can be expanded in a sum of inertial modes. Finally, we prove that two intriguing integral properties of inertial modes in rotating spheres and spheroids also extend to triaxial ellipsoids.
  • Cosection localization and the Quot scheme Quot S l (E)
    Item type: Journal Article
    Stark, Samuel (2022)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Let E be a locally free sheaf of rank r on a smooth projective surface S. The Quot scheme QuotSl(E) of length l coherent sheaf quotients of E is a natural higher-rank generalization of the Hilbert scheme of l points of S. We study the virtual intersection theory of this scheme. If C⊂ S is a smooth canonical curve, we use cosection localization to show that the virtual fundamental class of QuotSl(E) is (-1)l times the fundamental class of the smooth subscheme QuotCl(E|C)⊂ QuotSl(E). We then prove a structure theorem for virtual tautological integrals over QuotSl(E). From this, we deduce, among other things, the equality of virtual Euler characteristics χvir(QuotSl(E))=χvir(QuotSl(O⊕ r)).
  • Contact lines on stretched soft solids: modelling anisotropic surface stresses
    Item type: Journal Article
    Heyden, Stefanie; Bain, Nicolas; Xu, Qin; et al. (2021)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al. 2018 Soft Matter 14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al., but revise values of the surface elastic constants.
  • Nearly constant Q dissipative models and wave equations for general viscoelastic anisotropy
    Item type: Journal Article
    Hao, Qi; Greenhalgh, Stewart (2021)
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    The quality factor (Q) links seismic wave energy dissipation to physical properties of the Earth's interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common assumption in practice for seismic Q inversions. Although exactly and nearly constant Q dissipative models are proposed in the literature, it is inconvenient to obtain constant Q wave equations in differential form, which explicitly involve a specified Q parameter. In our recent research paper, we proposed a novel weighting function method to build the first- and second-order nearly constant Q dissipative models. Of importance is the fact that the wave equations in differential form for these two models explicitly involve a specified Q parameter. This behaviour is beneficial for time-domain seismic waveform inversion for Q, which requires the first derivative of wavefields with respect to Q parameters. In this paper, we extend the first- and second-order nearly constant Q models to the general viscoelastic anisotropic case. We also present a few formulations of the nearly constant Q viscoelastic anisotropic wave equations in differential form.
Publications1 - 10 of 81