Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSelf Organization and Self Avoiding Limit Cycles
347
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a small number of mobile particles travel. These trajectories are self-avoiding and non-intersecting, and their relationship to self-avoiding random walks is explored. Near $rho=0.5$ the distribution of path lengths becomes power-law like up to some cutoff length, suggesting a possible critical state.
rate research
Read More
We study the dynamics of exchange value in a system composed of many interacting agents. The simple model we propose exhibits cooperative emergence and collapse of global value for individual goods. We demonstrate that the demand that drives the value exhibits non Gaussian fat tails and typical fluctuations which grow with time interval with a Hurst exponent of 0.7.
We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] times [0, L]$ on the square lattice ${mathbb Z}^2$. The number of distinct walks is known to grow as $lambda^{L^2+o(L^2)}$. We estimate $lambda = 1.744550 pm 0.000005$ as well as obtaining strict upper and lower bounds, $1.628 < lambda < 1.782.$ We give exact results for the number of SAW of length $2L + 2K$ for $K = 0, 1, 2$ and asymptotic results for $K = o(L^{1/3})$. We also consider the model in which a weight or {em fugacity} $x$ is associated with each step of the walk. This gives rise to a canonical model of a phase transition. For $x < 1/mu$ the average length of a SAW grows as $L$, while for $x > 1/mu$ it grows as $L^2$. Here $mu$ is the growth constant of unconstrained SAW in ${mathbb Z}^2$. For $x = 1/mu$ we provide numerical evidence, but no proof, that the average walk length grows as $L^{4/3}$. We also consider Hamiltonian walks under the same restriction. They are known to grow as $tau^{L^2+o(L^2)}$ on the same $L times L$ lattice. We give precise estimates for $tau$ as well as upper and lower bounds, and prove that $tau < lambda.$
An explicit expression is derived for the scattering function of a self-avoiding polymer chain in a $d$-dimensional space. The effect of strength of segment interactions on the shape of the scattering function and the radius of gyration of the chain is studied numerically. Good agreement is demonstrated between experimental data on dilute solutions of several polymers and results of numerical simulation.
A nonadditive generalization of Klimontovichs S-theorem [G. B. Bagci, Int.J. Mod. Phys. B 22, 3381 (2008)] has recently been obtained by employing Tsallis entropy. This general version allows one to study physical systems whose stationary distributions are of the inverse power law in contrast to the original S-theorem, which only allows exponential stationary distributions. The nonadditive S-theorem has been applied to the modified Van der Pol oscillator with inverse power law stationary distribution. By using nonadditive S-theorem, it is shown that the entropy decreases as the system is driven out of equilibrium, indicating self-organization in the system. The allowed values of the nonadditivity index $q$ are found to be confined to the regime (0.5,1].
We consider self-avoiding walks terminally attached to a surface at which they can adsorb. A force is applied, normal to the surface, to desorb the walk and we investigate how the behaviour depends on the vertex of the walk at which the force is applied. We use rigorous arguments to map out some features of the phase diagram, including bounds on the locations of some phase boundaries, and we use Monte Carlo methods to make quantitative predictions about the locations of these boundaries and the nature of the various phase transitions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
