Tue, 22 Feb 2022

14:00 - 15:00
Virtual

X-centrality, node immunization, and eigenvector localization

Leo Torres
(Max Planck Institute)
Abstract

 

The non-backtracking matrix and its eigenvalues have many applications in network science and graph mining. For example, in network epidemiology, the reciprocal of the largest eigenvalue of the non-backtracking matrix is a good approximation for the epidemic threshold of certain network dynamics. In this work, we develop techniques that identify which nodes have the largest impact on the leading non-backtracking eigenvalue. We do so by studying the behavior of the spectrum of the non-backtracking matrix after a node is removed from the graph, which can be thought of as immunizing a node against the spread of disease. From this analysis we derive a centrality measure which we call X-degree, which is then used to predict which nodes have a large influence in the epidemic threshold. Finally, we discuss work currently in progress on connections with eigenvector localization and percolation theory.

Wed, 22 Apr 2015
14:00
C4

Understanding crack patterns: mud, lava, permafrost and crocodiles

Lucas Goehring
(Max Planck Institute)
Abstract

Contraction cracks form captivating patterns such as those seen in dried mud or the polygonal networks that cover the polar regions of Earth and Mars. These patterns can be controlled, for example in the artistic craquelure sometimes found in pottery glazes. More practically, a growing zoo of patterns, including parallel arrays of cracks, spiral cracks, wavy cracks, lenticular or en-passant cracks, etc., are known from simple experiments in thin films – essentially drying paint – and are finding application in surfaces with engineered properties. Through such work we are also learning how natural crack patterns can be interpreted, for example in the use of dried blood droplets for medical or forensic diagnosis, or to understand how scales develop on the heads of crocodiles.

I will discuss mud cracks, how they form, and their use as a simple laboratory analogue system. For flat mud layers I will show how sequential crack formation leads to a rectilinear crack network, with cracks meeting each other at roughly 90°. By allowing cracks to repeatedly form and heal, I will describe how this pattern evolves into a hexagonal pattern. This is the origin of several striking real-world systems: columnar joints in starch and lava; cracks in gypsum-cemented sand; and the polygonal terrain in permafrost. Finally, I will turn to look at crack patterns over uneven substrates, such as paint over the grain of wood, or on geophysical scales involving buried craters, and identify when crack patterns are expected to be dominated by what lies beneath them. In exploring all these different situations I will highlight the role of energy release in selecting the crack patterns that are seen.

Tue, 16 Jul 2013

10:15 - 11:15
OCCAM Common Room (RI2.28)

Coarsening rates for the dynamics of interacting slipping droplets

Georgy Kitavtsev
(Max Planck Institute)
Abstract

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON TUESDAY     *****

Reduced ODE models describing coarsening dynamics of droplets in nanometric polymer film interacting on solid substrate in the presence of large slippage at the liquid/solid interface are derived from one-dimensional lubrication equations. In the limiting case of the infinite slip length corresponding to the free suspended films a collision/absorption model then arises and is solved explicitly. The exact collision law is derived. Existence of a threshold at which the collision rates switch from algebraic to exponential ones is shown.

*****     PLEASE NOTE THIS SEMINAR TAKES PLACE ON TUESDAY     *****

Mon, 04 May 2009

12:00 - 13:00
L3

(0,2) Landau-Ginzburg Models and Residues

Ilarion Melnikov
(Max Planck Institute)
Abstract
Abstract: I will discuss techniques for the computation of correlators in (0,2) Landau-Ginzburg models.  After introducing these theories from the point of view of heterotic compactifications, I will describe the associated half-twisted models and their basic algebraic structure.  This structure enables direct computation of correlators and suggests a generalization of the Grothendieck residue.
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