ELECTROPHORESIS OF TOPOLOGICALLY NONTRIVIAL MACROMOLECULES: MATHEMATICAL AND COMPUTATIONAL STUDIES

1996 ◽  
Vol 07 (02) ◽  
pp. 217-271 ◽  
Author(s):  
HWA A. LIM
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Numerical Models ◽  
Thermal Fluctuations ◽  
Metropolis Algorithm ◽  
Three Dimensions ◽  
Square Lattice ◽  
Computational Studies ◽  
Cubic Lattice

Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are presented. The molecules are modeled as polygons residing on a square lattice and a cubic lattice whereas the electrophoretic media of obstacle network are simulated by removing vertices from the lattices at random. The dynamics of the polymeric molecules are modeled by configurational readjustments of segments of the polygons. Configurational readjustments arise from thermal fluctuations and they correspond to piecewise reptation in the simulations. A Metropolis algorithm is introduced to simulate these dynamics, and the algorithms are proven to be reversible and ergodic. Monte Carlo simulations of steady field random obstacle electrophoresis are performed and the results are presented.

Exact site-percolation probability on the square lattice

2021 ◽  
Author(s):  
Stephan Mertens
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Percolation Threshold ◽  
Percolation Cluster ◽  
Square Lattice ◽  
Site Percolation ◽  
Exact Probability ◽  
Percolation Probability ◽  
A Site ◽  
Time And Space Complexity

Abstract We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

Magnetic Properties Study of the Nano-Alloy Fe1+xCo1−x by Monte-Carlo Simulations

SPIN ◽  
2019 ◽  
Vol 09 (01) ◽  
pp. 1950002 ◽  
Author(s):  
I. El Housni ◽  
H. Labrim ◽  
N. El Mekkaoui ◽  
S. Idrissi ◽  
R. Khalladi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Magnetic Properties ◽  
Monte Carlo Simulations ◽  
Phase Diagrams ◽  
Ground State ◽  
Exchange Coupling ◽  
Hysteresis Loops ◽  
Metropolis Algorithm ◽  
Spintronic Devices ◽  
Temperature Exchange

Motivated by spintronic devices and their applications, we engineer a model to investigate the magnetic properties of the magnetic nano-alloy Fe[Formula: see text]Co[Formula: see text]. Where [Formula: see text] is the fraction of iron atoms Fe substituted by the cobalt Co atoms, [Formula: see text] corresponds to 50% Fe atoms and 50% Co atoms, this compound is then called equiatomic FeCo. The purpose of this work is to apply the Monte-Carlo Simulations (MCS), under Metropolis algorithm to predict the magnetic properties of such system. In a first step, we propose a model describing this system including different exchange coupling interactions. Then, we establish and analyze the ground state phase diagrams, in different planes. For non-null temperature values, applied MCS under the Metropolis algorithm. The behavior of both the magnetizations and the susceptibilities are illustrated as a function of temperature. Also the effect of the different exchange coupling interactions is studied and discussed. The hysteresis loops are presented and analyzed for specific values of temperature, exchange coupling interactions and concentrations.

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 RELAXATION UNDER OUTFLOW DYNAMICS WITH RANDOM SEQUENTIAL UPDATING

2005 ◽  
Vol 16 (11) ◽  
pp. 1771-1783 ◽  
Author(s):  
SYLWIA KRUPA ◽  
KATARZYNA SZNAJD-WERON
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Square Lattice ◽  
One Dimensional ◽  
Sequential Updating ◽  
The Mean

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule.

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