Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices

Theoretical Physic

Effect of defects on reaction of NiO surface with Pb-contained solution

In order to understand the role of defects in chemical reactions, we used two types of samples, which are molecular beam epitaxy (MBE) grown NiO(001) film on Mg(001) substrate as the defect free NiO prototype and NiO grown on Ni(110) single crystal as the one with defects. In-situ observations for oxide-liquid interfacial structure and surface morphology were performed for both samples in water and Pb-contained solution using high-resolution X-ray reflectivity and atomic force microscopy. For the MBE grown NiO, no significant changes were detected in the high-resolution X-ray reflectivity data with monotonic increase in roughness. Meanwhile, in the case of native grown NiO on Ni(110), significant changes in both the morphology and atomistic structure at the interface were observed when immersed in water and Pb-contained solution. Our results provide simple and direct experimental evidence of the role of the defects in chemical reaction of oxide surfaces with both water and Pb-contained solution.ope

Árgyil és Tündér Ilona : eredeti nép rege, dalokkal, és tánczcczal 3 felvonásban - irta Szigligeti E. - zenéjét Doppler Károly és Medgyesi Nándor

Debreczeni Szinház. Szombaton, april hó 2-kán bérletszünetben elöször adatik.Debreceni Egyetem Egyetemi és Nemzeti Könyvtá

Infinitesimal rigidity for non-Euclidean bar-joint frameworks

The minimal innitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R2, ||.||q) are characterised in terms of (2,2)-tight graphs. Specifically, a generically placed bar-joint framework (G,p) in the plane is minimally infinitesimally rigid with respect to a non-Euclidean lq norm if and only if the underlying graph G = (V,E) contains 2|V|-2 edges and every subgraph H = (V (H),E(H)) contains at most 2|V(H)|-2 edges