scholarly journals Geometric order parameters derived from the Voronoi tessellation show signatures of the jamming transition

Soft Matter ◽  
2016 ◽  
Vol 12 (4) ◽  
pp. 1248-1255 ◽  
Author(s):  
Peter K. Morse ◽  
Eric I. Corwin
Keyword(s):  
Power Law ◽  
Voronoi Tessellation ◽  
Order Parameters ◽  
Jamming Transition ◽  
Voronoi Tesselation ◽  
Clear Signature ◽  
Geometric Order

Order parameters derived from the Voronoi tesselation show a clear signature of the jamming transition with power law scaling.

scholarly journals Tail Bounds for the Stable Marriage of Poisson and Lebesgue

2009 ◽  
Vol 61 (6) ◽  
pp. 1279-1299 ◽  
Author(s):  
Christopher Hoffman ◽  
Alexander E. Holroyd ◽  
Yuval Peres
Keyword(s):  
Phase Transition ◽  
Lower Bounds ◽  
Power Law ◽  
Critical Case ◽  
Voronoi Tessellation ◽  
Upper Bounds ◽  
Stable Marriage ◽  
Marriage Problem ◽  
Stable Allocation ◽  
Typical Site

Abstract Let 𝚵 be a discrete set in ℝd. Call the elements of 𝚵 centers. The well-known Voronoi tessellation partitions ℝd into polyhedral regions (of varying volumes) by allocating each site of ℝd to the closest center. Here we study allocations of ℝd to 𝚵 in which each center attempts to claima region of equal volume α.We focus on the case where 𝚵 arises from a Poisson process of unit intensity. In an earlier paper by the authors it was proved that there is a unique allocation which is stable in the sense of the Gale–Shapley marriage problem. We study the distance X from a typical site to its allocated center in the stable allocation.The model exhibits a phase transition in the appetite α. In the critical case α = 1 we prove a power law upper bound on X in dimension d = 1. (Power law lower bounds were proved earlier for all d). In the non-critical cases α < 1 and α > 1 we prove exponential upper bounds on X.

scholarly journals Jamming transition evinced by Voronoi Tesselation

2017 ◽  
Vol 140 ◽  
pp. 16002 ◽  
Author(s):  
Eduardo Boaventura ◽  
Fernando Ducha ◽  
A.P.F Atman
Keyword(s):  
Jamming Transition ◽  
Voronoi Tesselation

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

1968 ◽  
Vol 11 (1) ◽  
pp. 169-178 ◽  
Author(s):  
Alan Gill ◽  
Charles I. Berlin
Keyword(s):  
Power Law ◽  
Response Magnitude ◽  
Single Units ◽  
Spectral Content ◽  
Hearing Sensitivity ◽  
Subjective Magnitude ◽  
Orderly Fashion ◽  
Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

How Useful is the Power Law of Practice for Recognizing Practice in Concentration Tests?

2007 ◽  
Vol 23 (3) ◽  
pp. 157-165 ◽  
Author(s):  
Carmen Hagemeister
Keyword(s):  
Logistic Regression ◽  
Reaction Time ◽  
Power Law ◽  
Error Rate ◽  
Reaction Times ◽  
Practice Effect ◽  
Practice Effects ◽  
Rate Decrease ◽  
Small Practice

Abstract. When concentration tests are completed repeatedly, reaction time and error rate decrease considerably, but the underlying ability does not improve. In order to overcome this validity problem this study aimed to test if the practice effect between tests and within tests can be useful in determining whether persons have already completed this test. The power law of practice postulates that practice effects are greater in unpracticed than in practiced persons. Two experiments were carried out in which the participants completed the same tests at the beginning and at the end of two test sessions set about 3 days apart. In both experiments, the logistic regression could indeed classify persons according to previous practice through the practice effect between the tests at the beginning and at the end of the session, and, less well but still significantly, through the practice effect within the first test of the session. Further analyses showed that the practice effects correlated more highly with the initial performance than was to be expected for mathematical reasons; typically persons with long reaction times have larger practice effects. Thus, small practice effects alone do not allow one to conclude that a person has worked on the test before.

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law
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