ISTA Research Explorer (Institute of Science and Technology Austria)
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Glacier-atmosphere interactions and feedbacks in high-mountain regions - A review
No full textMountain glaciers are among the natural systems most vulnerable to climate change. However, their interactions with the atmosphere are complex and not fully understood. These interactions can trigger rapid adjustments and climate feedbacks that either amplify or attenuate atmospheric signals, influencing both glacier response and large-scale atmospheric circulation. Observing this functional coupling in nature is challenging because the key processes occur over a wide range of spatial and temporal scales. However, recent advances in observational techniques and modeling have provided new insights into these interactions. In this review, we summarize the current state of knowledge on glacier-atmosphere interactions in high-mountain regions at different scales, and highlight recent advances in observational and numerical modeling. We also highlight important knowledge gaps and outline future research directions to improve the prediction of glacier change in a warming world
Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions
No full textWe prove the convergence of a modified Jordan–Kinderlehrer–Otto scheme to a solution
to the Fokker–Planck equation in Ω e R^d with general—strictly positive and temporally
constant—Dirichlet boundary conditions. We work under mild assumptions on the domain,
the drift, and the initial datum. In the special case where Ω is an interval in R1, we prove
that such a solution is a gradient flow—curve of maximal slope—within a suitable space of
measures, endowed with a modified Wasserstein distance. Our discrete scheme and modified
distance draw inspiration from contributions by A. Figalli and N. Gigli [J. Math. Pures
Appl. 94, (2010), pp. 107–130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41–88]
on an optimal-transport approach to evolution equations with Dirichlet boundary conditions.
Similarly to these works, we allow the mass to flow from/to the boundary ∂Ω throughout
the evolution. However, our leading idea is to also keep track of the mass at the boundary
by working with measures defined on the whole closure Ω . The driving functional is a
modification of the classical relative entropy that also makes use of the information at the
boundary. As an intermediate result, when Ω is an interval in R1, we find a formula for the
descending slope of this geodesically nonconvex functional
Optimal decay of eigenvector overlap for non-Hermitian random matrices
No full textWe consider the standard overlap (math formular) of any bi-orthogonal family of left and right eigenvectors of a large random matrix X with centred i.i.d. entries and we prove that it decays as an inverse second power of the distance between the corresponding eigenvalues. This extends similar results for the complex Gaussian ensemble from Bourgade and Dubach [15], as well as Benaych-Georges and Zeitouni [13], to any i.i.d. matrix ensemble in both symmetry classes. As a main tool, we prove a two-resolvent local law for the Hermitisation of X uniformly in the spectrum with optimal decay rate and optimal dependence on the density near the spectral edge
On the size of chromatic Delaunay mosaics
No full textGiven a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications
The Hamilton space of pseudorandom graphs
No full textWe show that if n is odd and p>=Clog n/n, then with high probability Hamilton cycles in G(n,p) span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n vertices and minimum degree n/2+C for sufficiently large constant C, span its cycle space