Hybrid journal (It can contain Open Access articles) ISSN (Print) 1687-1200 - ISSN (Online) 1687-1197 Published by Oxford University Press[406 journals]

Authors:Olson D; Ortner C. Pages: 297 - 337 Abstract: AbstractWe formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural phonon stability assumption, we quantify the decay of the long-range elastic fields with increasing distance from the defect. These decay estimates are an essential ingredient in quantifying approximation errors in coarse-grained models and in the construction of optimal numerical methods for approximating crystalline defects. PubDate: Wed, 18 Jan 2017 00:00:00 GMT DOI: 10.1093/amrx/abw012 Issue No:Vol. 2017, No. 2 (2017)

Authors:Blanc X; Josien M. Pages: 338 - 385 Abstract: AbstractWe study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, and Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show numerically and mathematically that if the distances between particles remain bounded, it is not the case any more when there are shocks at least for a convex nearest-neighbor interaction potential with convex derivative. PubDate: Wed, 22 Feb 2017 00:00:00 GMT DOI: 10.1093/amrx/abx001 Issue No:Vol. 2017, No. 2 (2017)

Authors:Zuily C. Pages: 386 - 401 Abstract: AbstractWe show that resonant states in scattering on asymptotically hyperbolic manifolds that are analytic near conformal infinity have analytic radiation patterns at infinity. On even asymptotically hyperbolic manifolds, we also show that smooth solutions of Vasy operators with analytic coefficients are also analytic. That answers a question of Zworski ([14] Conjecture 2). The proof is based on previous results of Baouendi–Goulaouic and Bolley–Camus–Hanouzet, and for convenience of the reader, we present an outline of the proof of the latter. PubDate: Mon, 27 Feb 2017 00:00:00 GMT DOI: 10.1093/amrx/abx002 Issue No:Vol. 2017, No. 2 (2017)

Authors:Schmuck M. Pages: 402 - 430 Abstract: AbstractWe investigate well-accepted formulations describing charge transport in composite cathodes of batteries. Our upscaling of carefully selected microscopic equations shows three main features: A novel set of six equations equipped with nine effective parameters which systematically couple the microscale to the macroscale.The coupling of transport and flow equations allows us to account for three scales: pore scale, Darcy scale, and macroscale.The upscaled equations take phase separation during Li-intercalation into account as well as specific particle configurations.The wide range of applications and interest in energy storage devices makes these results a promising tool to study the influence of the microstructure on current–voltage characteristics and to optimize cathode designs. PubDate: Wed, 19 Apr 2017 00:00:00 GMT DOI: 10.1093/amrx/abx003 Issue No:Vol. 2017, No. 2 (2017)

Authors:Gustafson S; Le Coz S, Tsai T. Pages: 431 - 487 Abstract: AbstractWe study the stability of the cnoidal, dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D cubic nonlinear Schrödinger equations. First, we give global variational characterizations of each of these periodic waves, which in particular provide alternate proofs of their orbital stability with respect to same-period perturbations, restricted to certain subspaces. Second, we prove the spectral stability of the cnoidal waves (in a certain parameter range) and snoidal waves against same-period perturbations, thus providing an alternate proof of this (known) fact, which does not rely on complete integrability. Third, we give a rigorous version of a formal asymptotic calculation of Rowlands to establish the instability of a class of real-valued periodic waves in 1D, which includes the cnoidal waves of the 1D cubic focusing nonlinear Schrödinger equation, against perturbations with period a large multiple of their fundamental period. Finally, we develop a numerical method to compute the minimizers of the energy with fixed mass and momentum constraints. Numerical experiments support and complete our analytical results. PubDate: Thu, 15 Jun 2017 00:00:00 GMT DOI: 10.1093/amrx/abx004 Issue No:Vol. 2017, No. 2 (2017)

Authors:Dondl PW; Dorey P, Rösler F. Pages: 271 - 296 Abstract: AbstractWe are concerned with the non-normal Schrödinger operator H=−Δ+V on L2(Rn), where V∈Wloc1,∞(Rn) and ReV(x)≥c∣x∣2−d for some c,d>0. The spectrum of this operator is discrete and its real part is bounded below by −d. In general, the ε-pseudospectrum of H will have an unbounded component for any ε>0 and thus will not approximate the spectrum in a global sense.By exploiting the fact that the semigroup e−tH is immediately compact, we show a complementary result, namely that for every δ>0, R>0 there exists an ε>0 such that the ε-pseudospectrum σε(H)⊂{z:Rez≥R}∪⋃λ∈σ(H){z:∣z−λ∣<δ}. In particular, the unbounded part of the pseudospectrum escapes towards +∞ as ε decreases. In addition, we give two examples of non-selfadjoint Schrödinger operators outside of our class and study their pseudospectra in more detail. PubDate: Wed, 21 Dec 2016 00:00:00 GMT DOI: 10.1093/amrx/abw011 Issue No:Vol. 2017, No. 2 (2016)