RANDOM MULTIPLICATIVE RESPONSE FUNCTIONS IN GRANULAR CONTACT NETWORKS

2001 ◽  
Vol 04 (04) ◽  
pp. 523-533
Author(s):  
CRISTIAN F. MOUKARZEL
Keyword(s):  
Critical Point ◽  
Power Law ◽  
Applied Pressure ◽  
External Pressure ◽  
Contact Network ◽  
Green Functions ◽  
Response Functions ◽  
Power Law Distribution ◽  
Granular Packing ◽  
Multiplicative Processes

The contact network of a frictionless polydisperse granular packing is isostatic in the limit of low applied pressure. It is argued here that, on disordered isostatic networks, displacement–displacement and stress–stress static Green functions are described by random multiplicative processes and have a truncated power-law distribution, with a cut-off that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the abovementioned anomalous properties disappear because Green functions now have a bounded distribution. Thus, the low-pressure, isostatic, limit is a critical point.

Summary

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Critical Point ◽  
Power Law ◽  
Fossil Record ◽  
Large Scale ◽  
Extinction Rate ◽  
Mass Extinctions ◽  
Power Law Distribution ◽  
Scale Free ◽  
Extinction Events ◽  
Fossil Data

In this book we have studied a large number of recent quantitative models aimed at explaining a variety of large-scale trends seen in the fossil record. These trends include the occurrence of mass extinctions, the distribution of the sizes of extinction events, the distribution of the lifetimes of taxa, the distribution of the numbers of species per genus, and the apparent decline in the average extinction rate. None of the models presented match all the fossil data perfectly, but all of them offer some suggestion of possible mechanisms which may be important to the processes of extinction and origination. In this chapter we conclude our review by briefly summarizing the properties and predictions of each of the models once more. Much of the interest in these models has focused on their ability (or lack of ability) to predict the observed values of exponents governing distributions of a number of quantities. In Table 7.1 we summarize the values of these exponents for each of the models. Most of the models we have described attempt to provide possible explanations for a few specific observations. (1) The fossil record appears to have a power-law (i.e., scale-free) distribution of the sizes of extinction events, with an exponent close to 2 (section 1.2.2.1). (2) The distribution of the lifetimes of genera also appears to follow a power law, with exponent about 1.7 (section 1.2.2.4). (3) The number of species per genus appears to follow a power law with exponent about 1.5 (section 1.2.3.1). One of the first models to attempt an explanation of these observations was the NK model of Kauffman and co-workers. In this model, extinction is driven by revolutionary avalanches. When tuned to the critical point between chaotic and frozen regimes, the model displays a power-law distribution of avalanche sizes with an exponent of about 1. It has been suggested that this could in turn lead to a power-law distribution of the sizes of extinction events, although the value of 1 for the exponent is not in agreement with the value 2 measured in the fossil extinction record.

scholarly journals Micromechanics of slow granular flows

2021 ◽  
Vol 249 ◽  
pp. 03043
Author(s):  
Ravi Gautam ◽  
Prabhu R. Nott
Keyword(s):  
Power Law ◽  
Mechanical Response ◽  
Rate Of Change ◽  
Power Law Distribution ◽  
Stick Slip ◽  
Granular Packing ◽  
Large Fluctuations ◽  
Long Time ◽  
Macroscopic Motion ◽  
Dynamics Simulations

It has been contemplated for a long time that dense granular materials flow in a stick-slip manner, and large fluctuations in the stresses are associated with it. However, the particle scale mechanics for this type of macroscopic motion has not been understood so far. We have analyzed the time evolution of contact networks from particle dynamics simulations and found that the rate of change of elastic energy of the packing can distinguish the stick regimes and the slip events. The isostatic criterion (number of contacts for a minimally stable particle) has been used to construct a cascade failure mechanism which reveals that the effect of the random breaking of contacts due to applied shear can be system-spanning for some cases. The size of the cascade failures follows a power law that explains experimentally observed large fluctuations is stresses. We expect that this power law distribution can connect the microstructure of a granular packing to its mechanical response.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

2021 ◽  
Author(s):  
David A Garcia ◽  
Gregory Fettweis ◽  
Diego M Presman ◽  
Ville Paakinaho ◽  
Christopher Jarzynski ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Single Molecule ◽  
Power Law ◽  
Dwell Time ◽  
Specific Binding ◽  
Power Law Distribution ◽  
Single Molecule Level ◽  
Binding Behavior ◽  
Chromatin Template ◽  
Nuclear Domains

Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

scholarly journals Explaining the power-law distribution of human mobility through transportationmodality decomposition

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Kai Zhao ◽  
Mirco Musolesi ◽  
Pan Hui ◽  
Weixiong Rao ◽  
Sasu Tarkoma
Keyword(s):  
Power Law ◽  
Human Mobility ◽  
Power Law Distribution

MASS FUNCTION OF HALOS: A NEW ANALYTICAL APPROACH

2004 ◽  
Vol 13 (07) ◽  
pp. 1345-1349 ◽  
Author(s):  
JOSÉ A. S. LIMA ◽  
LUCIO MARASSI
Keyword(s):  
Power Law ◽  
Free Parameter ◽  
Analytical Approach ◽  
Mass Function ◽  
New Method ◽  
Power Law Distribution ◽  
The Press ◽  
The Universe ◽  
Special Case

A generalization of the Press–Schechter (PS) formalism yielding the mass function of bound structures in the Universe is given. The extended formula is based on a power law distribution which encompasses the Gaussian PS formula as a special case. The new method keeps the original analytical simplicity of the PS approach and also solves naturally its main difficult (the missing factor 2) for a given value of the free parameter.

scholarly journals Assessing the power law distribution of TGFs

2011 ◽  
Vol 116 (A10) ◽  
pp. n/a-n/a ◽  
Author(s):  
Andrew B. Collier ◽  
Thomas Gjesteland ◽  
Nikolai Østgaard
Keyword(s):  
Power Law ◽  
Power Law Distribution

scholarly journals Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

2007 ◽  
Vol 3 (S247) ◽  
pp. 279-287
Author(s):  
Patrick Antolin ◽  
Kazunari Shibata ◽  
Takahiro Kudoh ◽  
Daiko Shiota ◽  
David Brooks
Keyword(s):  
Power Law ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Power Law Distribution ◽  
Longitudinal Modes ◽  
Heating Mechanism ◽  
Set Up ◽  
Power Law Index ◽  
Power Law Distributions ◽  
Release Processes

AbstractAlfvén waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is the nanoflare-reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfvén waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-D MHD code. The obtained coronae differ in many aspects, for instance, in the simulated intensity profile that Hinode/XRT would observe. The intensity histograms display power law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

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