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The recent article `Satellite conjunction analysis and the false confidence theorem' (Balch, Martin, and Ferson, 2019, Proceedings of the Royal Society, Series A) points to certain difficulties with Bayesian analysis when used for models…
We construct an open set $\Omega\subset\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik-Schnirelmann…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft…
We find a new set of exact solutions to Maxwell's equations in space--time varying materials, where the refractive index is constant, while the impedance exhibits effective motion, i.e. it is a function of $x-vt$. We find that waves…
We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…
In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…
We present a new model for time evolution of fast magnetic reconnection in free space, which is characterized by self-similarity. Reconnection triggered by locally enhanced resistivity assumed at the center of the current sheet can…
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…
We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic…
We have found that the expansion of the universe has immense consequences on our local systems. We present a model based on cosmic expansion that fits well with observation. The close approach problem inflicting tidal theory is averted in…
The long-term evolution of epidemic processes depends crucially on the structure of contact networks. As empirical evidence indicates that human populations exhibit strong community organization, we investigate here how such mesoscopic…
Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused…
We consider expanding systems with invariant measures that are uniformly expanding everywhere except on a small measure set and show that the limiting statistics of hitting times for zero measure sets are compound Poisson provided the…
In contrast to extensively studied defects in traditional materials, we report here for the first time a systematic investigation of the formation mechanism of intrinsic defects in self-assembled peptide nanostructures. The Monte Carlo…
Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, applied fields or in quenches to the ordered phase. In equilibrium pairs of defects coarsen and annihilate as the uniform ground state…
We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on…
In this paper we present numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a…
Network diffusion models are used to study disease transmission, information spread, technology adoption, and other socio-economic processes. We show that estimates of these diffusions are highly non-robust to mismeasurement. First, even…