scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

MONTE CARLO SIMULATION OF ACTIN FILAMENT BASED CELL MOTILITY

2003 ◽  
Vol 17 (29) ◽  
pp. 5597-5611 ◽  
Author(s):  
K. -H. HERRMANN ◽  
S. V. M. SATYANARAYANA ◽  
V. SRIDHAR ◽  
K. P. N. MURTHY
Keyword(s):  
Monte Carlo ◽  
Cell Motility ◽  
Actin Polymerization ◽  
Monte Carlo Step ◽  
Optimal Choice ◽  
Square Lattice ◽  
Cell Velocity ◽  
Model Cell ◽  
Small Times ◽  
Remarkable Agreement

Cell motility resulting from actin polymerization is modeled on a two-dimensional square lattice. The treadmilling of actin filaments, formation of lamellipodia, protrusion and motility of the model cell are studied using Monte Carlo simulations. The grid space of the square lattice and the Monte Carlo step are related to length and time scales of the problem. The average velocity computed with this prescription from the simulations shows a remarkable agreement with the experimental velocity of a keratocyte. The model cell captures the essential aspects of treadmilling based motility. The movement of the model cell is diffusive for small times and exhibits a cross over to polymerization driven drift for large times. The studies on the parameter sensitivity of cell velocity indicated that the optimal choice of number of monomers, the number of filaments, the rate of depolymerization and the monomer diffusion leads to large velocities. The cell velocity distribution is found to be Gaussian and is in agreement with some of the experimental work.

scholarly journals UNIVERSAL FINITE-SIZE-SCALING FUNCTIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 287-294 ◽  
Author(s):  
YUTAKA OKABE ◽  
MACOTO KIKUCHI
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Order Parameter ◽  
Finite Size ◽  
Square Lattice ◽  
Parameter Distribution ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Regular Lattices

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.

scholarly journals RESHUFFLING SPINS WITH SHORT RANGE INTERACTIONS: WHEN SOCIOPHYSICS PRODUCES PHYSICAL RESULTS

2005 ◽  
Vol 16 (10) ◽  
pp. 1507-1517 ◽  
Author(s):  
A. O. SOUSA ◽  
K. MALARZ ◽  
S. GALAM
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Nonlinear Behavior ◽  
Opinion Dynamics ◽  
Monte Carlo Step ◽  
Square Lattice ◽  
The Mean ◽  
Dynamics Models

Galam reshuffling introduced in opinion dynamics models, is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature TC≈3.09 [J/kB] is recovered almost exactly, it is proved to be different from both values, not reshuffled (TC =2/ arcsinh (1)≈2.27 [J/kB]) and mean-field (TC =4 [J/kB]). On this basis, gradual reshuffling is studied as function of 0≤p≤1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of TC as function of p is obtained and exhibits a nonlinear behavior. The simplest Solomon network realization is noted to reproduce Galam p =1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean field values.

NUMERICAL SIMULATION OF THE 1D AND 2D HUBBARD MODELS: FERMI LIQUID BEHAVIOR AND ITS BREAKDOWN

1988 ◽  
Vol 02 (05) ◽  
pp. 993-1003 ◽  
Author(s):  
S. Sorella ◽  
E. Tosatti ◽  
S. Baroni ◽  
R. Car ◽  
M. Parrinello
Keyword(s):  
Ground State ◽  
Fermi Liquid ◽  
Finite Size ◽  
Simulation Method ◽  
Square Lattice ◽  
Antiferromagnetic Order ◽  
Hubbard Models ◽  
Clear Sign ◽  
Liquid Behavior ◽  
Half Filling

The ground state of the 1D and of the 2D (square lattice) finite-size Hubbard model is investigated for variable filling using a novel quantum simulation method. We have studied up to 256 sites for both 1D and 2D. Away from half filling the 2D antiferromagnetic order is initially destroyed, albeit without any clear sign of a Fermi liquid behaviour. A metallic jump in n(k) appears only very far from half filling. In the 1D case, by contrast, a Fermi liquid-like jump in n(k) is obtained even very close to half filling.

scholarly journals Critical non-Hermitian skin effect

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Sen Mu ◽  
Jiangbin Gong
Keyword(s):  
Thermodynamic Limit ◽  
Skin Effect ◽  
Finite Size ◽  
System Size ◽  
Critical Systems ◽  
Anomalous Scaling ◽  
Lattice Systems ◽  
New Class ◽  
Rlc Circuit ◽  
Zero Coupling

Abstract Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

scholarly journals Size Effect in Grand-canonical Monte-Carlo Simulation of Solutions of Electrolyte

2019 ◽  
Vol 35 (2) ◽  
Author(s):  
Nguyen Viet Duc
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Size Effect ◽  
Chemical Potential ◽  
Finite Size ◽  
Simulation Method ◽  
Electrolyte Solutions ◽  
Finite Size Effect ◽  
Grand Canonical Monte Carlo ◽  
Grand Canonical

Abstract: A Grand-canonical Monte-Carlo simulation method is investigated. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts at different concentrations using the primitive ion model. We investigate how the finite size of the simulation box can influence statistical quantities of the salt system. Remarkably, the method works well down to a system as small as one salt molecule. Although the fluctuation in the statistical quantities increases as the system gets smaller, their average values remain equal to their bulk value within the uncertainty error. Based on this knowledge, the osmotic pressures of the electrolyte solutions are calculated and shown to depend linearly on the salt concentrations within the concentration range simulated. Chemical potential of ionic salt that can be used for simulation of these salts in more complex system are calculated. Keywords: GCMC, electrolyte solution simulation, primitive ion model, finite size effect.

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