scholarly journals RISE OF THE CENTRIST: FROM BINARY TO CONTINUOUS OPINION DYNAMICS

2008 ◽  
Vol 19 (09) ◽  
pp. 1459-1475 ◽  
Author(s):  
GEORGE A. BAKER ◽  
JAMES P. HAGUE
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Continuum Limit ◽  
Linear Chain ◽  
Opinion Dynamics ◽  
Memory Effects ◽  
Time Step ◽  
Binary Model ◽  
Long Time ◽  
The Continuum

We propose a model that extends the binary "united we stand, divided we fall" opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions on a linear chain. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.

scholarly journals Probabilistic Analysis of the Hard Rock Disintegration Process

10.14311/1041 ◽  
2008 ◽  
Vol 48 (4) ◽  
Author(s):  
K. Frydrýšek
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Hard Rock ◽  
Assessment Method ◽  
Contact Forces ◽  
Disintegration Process ◽  
Long Time ◽  
Structural Nonlinearities ◽  
Reaction Forces ◽  
Mathcad Software

This paper focuses on a numerical analysis of the hard rock (ore) disintegration process. The bit moves and sinks into the hard rock (mechanical contact with friction between the ore and the cutting bit) and subsequently disintegrates it. The disintegration (i.e. the stress-strain relationship, contact forces, reaction forces and fracture of the ore) is solved via the FEM (MSC.Marc/Mentat software) and SBRA (Simulation-Based Reliability Assessment) method (Monte Carlo simulations, Anthill and Mathcad software). The ore is disintegrated by deactivating the finite elements which satisfy the fracture condition. The material of the ore (i.e. yield stress, fracture limit, Young’s modulus and Poisson’s ratio), is given by bounded histograms (i.e. stochastic inputs which better describe reality). The results (reaction forces in the cutting bit) are also of stochastic quantity and they are compared with experimental measurements. Application of the SBRA method in this area is a modern and innovative trend in mechanics. However, it takes a long time to solve this problem (due to material and structural nonlinearities, the large number of elements, many iteration steps and many Monte Carlo simulations). Parallel computers were therefore used to handle the large computational needs of this problem. 

Time step error in diffusion Monte Carlo simulations: An empirical study

1987 ◽  
Vol 8 (4) ◽  
pp. 412-419 ◽  
Author(s):  
Stuart M. Rothstein ◽  
Narayan Patil ◽  
Jan Vrbik
Keyword(s):  
Monte Carlo ◽  
Empirical Study ◽  
Monte Carlo Simulations ◽  
Diffusion Monte Carlo ◽  
Time Step

Linear Chain of Coupled Fractional Oscillators: Response Dynamics and Its Continuum Limit

2007 ◽  
Author(s):  
B. N. Narahari Achar ◽  
Tanya Prozny ◽  
John W. Hanneken
Keyword(s):  
Continuum Limit ◽  
Equations Of Motion ◽  
Linear Chain ◽  
Harmonic Oscillators ◽  
Fractional Dynamics ◽  
Response Dynamics ◽  
Numerical Application ◽  
Diffusion Wave ◽  
A Chain ◽  
The Continuum

The standard model of a chain of simple harmonic oscillators of Condensed Matter Physics is generalized to a model of linear chain of coupled fractional oscillators in fractional dynamics. The set of integral equations of motion pertaining to the chain of harmonic oscillators is generalized by taking the integrals to be of arbitrary order according to the methods of fractional calculus to yield the equations of motion of a chain of coupled fractional oscillators. The solution is obtained by using Laplace transforms. The continuum limit of the equations is shown to yield the fractional diffusion-wave equation in one dimension. The solution and numerical application of the set of equations and the continuum limit there of are discussed.

scholarly journals Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition

2022 ◽  
Vol 2022 (1) ◽  
pp. 013402
Author(s):  
Xiang Li ◽  
Mauro Mobilia ◽  
Alastair M Rucklidge ◽  
R K P Zia
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Social Interaction ◽  
Monte Carlo Simulations ◽  
Network Structure ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Analysis ◽  
Long Time

Abstract We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents’ opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we investigate how the sizes of the communities and the degree of homophily/heterophily affect the network structure. In particular, we show that when the network is subject to enough heterophily, an ‘overwhelming transition’ occurs: individuals of the smaller community are overwhelmed by links from the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by the network’s total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network’s polarization when the group sizes and level of homophily vary.

Transition under noise in the Sznajd model on square lattice

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Social Behavior ◽  
Monte Carlo Simulations ◽  
Order Phase Transition ◽  
Opinion Dynamics ◽  
Two Dimensions ◽  
Square Lattice ◽  
Behavior Model ◽  
Second Order Phase Transition

In order to describe the formation of a consensus in human opinion dynamics, in this paper, we study the Sznajd model with probabilistic noise in two dimensions. The time evolution of this system is performed via Monte Carlo simulations. This social behavior model with noise presents a well defined second-order phase transition. For small enough noise q < 0.33 most agents end up sharing the same opinion.

scholarly journals Testing algorithms for critical slowing down

2018 ◽  
Vol 175 ◽  
pp. 02008 ◽  
Author(s):  
Guido Cossu ◽  
Peter Boyle ◽  
Norman Christ ◽  
Chulwoo Jung ◽  
Andreas Jüttner ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Topological Charge ◽  
Continuum Limit ◽  
Critical Slowing Down ◽  
Gauge Fields ◽  
Hybrid Monte Carlo ◽  
Slowing Down ◽  
Testing Algorithms ◽  
New Algorithms ◽  
The Continuum

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

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