Asymptotic shape of elastic networks

1995 ◽  
Vol 52 (7) ◽  
pp. 5404-5413 ◽  
Author(s):  
Z. Zhang ◽  
H. T. Davis ◽  
R. S. Maier ◽  
D. M. Kroll
Keyword(s):  
Elastic Networks ◽  
Asymptotic Shape

Fracture Growth in 2 d Elastic Networks with Born Model

1989 ◽  
Vol 10 (1) ◽  
pp. 7-13 ◽  
Author(s):  
H Yan ◽  
G Li ◽  
L. M Sander
Keyword(s):  
Elastic Networks ◽  
Born Model ◽  
Fracture Growth

Complexity and elastic networks

2010 ◽  
Vol 25 (3) ◽  
pp. e2
Author(s):  
Béla Suki
Keyword(s):  
Elastic Networks

scholarly journals Asymptotic shape of the convex hull of isotropic log-concave random vectors

2016 ◽  
Vol 75 ◽  
pp. 116-143 ◽  
Author(s):  
Apostolos Giannopoulos ◽  
Labrini Hioni ◽  
Antonis Tsolomitis
Keyword(s):  
Convex Hull ◽  
Random Vectors ◽  
Asymptotic Shape

The asymptotic shape of the branching random walk

1978 ◽  
Vol 10 (1) ◽  
pp. 62-84 ◽  
Author(s):  
J. D. Biggins
Keyword(s):  
Random Walk ◽  
Explicit Formula ◽  
Branching Process ◽  
Analogous Result ◽  
Convex Set ◽  
Branching Random Walk ◽  
Asymptotic Shape ◽  
Age Dependent ◽  
Watson Process

In a supercritical branching random walk on Rp, a Galton–Watson process with the additional feature that people have positions, let be the set of positions of the nth-generation people, scaled by the factor n–1. It is shown that when the process survives looks like a convex set for large n. An analogous result is established for an age-dependent branching process in which people also have positions. In certain cases an explicit formula for the asymptotic shape is given.

A Two-Dimensional Cellular Automaton Crystal with Irrational Density

2003 ◽  
Author(s):  
David Griffeath ◽  
Dean Hickerson
Keyword(s):  
Cellular Automaton ◽  
Asymptotic Density ◽  
Coarse Grain ◽  
Constant Density ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Empty Cell ◽  
Asymptotic Shape ◽  
Conway’S Game Of Life ◽  
Asymptotic Densities

We solve a problem posed recently by Gravner and Griffeath [4]: to find a finite seed A0 of 1s for a simple {0, l}-valued cellular automaton growth model on Z2 such that the occupied crystal An after n updates spreads with a two-dimensional asymptotic shape and a provably irrational density. Our solution exhibits an initial A0 of 2,392 cells for Conway’s Game Of Life from which An cover nT with asymptotic density (3 - √5/90, where T is the triangle with vertices (0,0), (-1/4,-1/4), and (1/6,0). In “Cellular Automaton Growth on Z2: Theorems, Examples, and Problems” [4], Gravner and Griffeath recently presented a mathematical framework for the study of Cellular Automata (CA) crystal growth and asymptotic shape, focusing on two-dimensional dynamics. For simplicity, at any discrete time n, each lattice site is assumed to be either empty (0) or occupied (1). Occupied sites after n updates grows linearly in each dimension, attaining an asymptotic density p within a limit shape L: . . . n-1 A → p • 1L • (1) . . . This phenomenology is developed rigorously in Gravner and Griffeath [4] for Threshold Growth, a class of monotone solidification automata (in which case p = 1), and for various nonmonotone CA which evolve recursively. The coarse-grain crystal geometry of models which do not fill the lattice completely is captured by their asymptotic density, as precisely formulated in Gravner and Griffeath [4]. It may happen that a varying “hydrodynamic” profile p(x) emerges over the normalized support L of the crystal. The most common scenario, however, would appear to be eq. (1), with some constant density p throughout L. All the asymptotic densities identified by Gravner and Griffeath are rational, corresponding to growth which is either exactly periodic in space and time, or nearly so. For instance, it is shown that Exactly 1 Solidification, in which an empty cell permanently joins the crystal if exactly one of its eight nearest (Moore) neighbors is occupied, fills the plane with density 4/9 starting from a singleton.

Intention and Body-Mood Engineering via Proactive Robot Moves in HRI

2015 ◽  
pp. 255-282 ◽  
Author(s):  
O. Can Görür ◽  
Aydan M. Erkmen
Keyword(s):  
Path Planning ◽  
Mobile Robots ◽  
Human Body ◽  
Mood Induction ◽  
Positive Mood ◽  
Focused Attention ◽  
Elastic Networks ◽  
Human Intention ◽  
Novel Concept ◽  
Intention Estimation

This chapter focuses on emotion and intention engineering by socially interacting robots that induce desired emotions/intentions in humans. The authors provide all phases that pave this road, supported by overviews of leading works in the literature. The chapter is partitioned into intention estimation, human body-mood detection through external-focused attention, path planning through mood induction and reshaping intention. Moreover, the authors present their novel concept, with implementation, of reshaping current human intention into a desired one, using contextual motions of mobile robots. Current human intention has to be deviated towards the new desired one by destabilizing the obstinance of human intention, inducing positive mood and making the “robot gain curiosity of human”. Deviations are generated as sequences of transient intentions tracing intention trajectories. The authors use elastic networks to generate, in two modes of body mood: “confident” and “suspicious”, transient intentions directed towards the desired one, choosing among intentional robot moves previously learned by HMM.

scholarly journals Multiple Elastic Networks With Time Delays for Early Fault Detection and Prognostics

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 129387-129396
Author(s):  
Dongliang Guo ◽  
Wen Yang ◽  
Fengbo Tao ◽  
Bing Song ◽  
Hui Liu ◽  
...  
Keyword(s):  
Fault Detection ◽  
Time Delays ◽  
Elastic Networks ◽  
Early Fault Detection

The asymptotic shape of the branching random walk

1978 ◽  
Vol 10 (01) ◽  
pp. 62-84 ◽  
Author(s):  
J. D. Biggins
Keyword(s):  
Random Walk ◽  
Explicit Formula ◽  
Branching Process ◽  
Analogous Result ◽  
Convex Set ◽  
Branching Random Walk ◽  
Asymptotic Shape ◽  
Age Dependent ◽  
Watson Process

In a supercritical branching random walk on R p , a Galton–Watson process with the additional feature that people have positions, let be the set of positions of the nth-generation people, scaled by the factor n –1. It is shown that when the process survives looks like a convex set for large n. An analogous result is established for an age-dependent branching process in which people also have positions. In certain cases an explicit formula for the asymptotic shape is given.

Sign in / Sign up

Export Citation Format

Share Document