ترغب بنشر مسار تعليمي؟ اضغط هنا

Preferential attachment growth model and nonextensive statistical mechanics

224   0   0.0 ( 0 )
 نشر من قبل Constantino Tsallis
 تاريخ النشر 2004
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce a two-dimensional growth model where every new site is located, at a distance $r$ from the barycenter of the pre-existing graph, according to the probability law $1/r^{2+alpha_G} (alpha_G ge 0)$, and is attached to (only) one pre-existing site with a probability $propto k_i/r^{alpha_A}_i (alpha_A ge 0$; $k_i$ is the number of links of the $i^{th}$ site of the pre-existing graph, and $r_i$ its distance to the new site). Then we numerically determine that the probability distribution for a site to have $k$ links is asymptotically given, for all values of $alpha_G$, by $P(k) propto e_q^{-k/kappa}$, where $e_q^x equiv [1+(1-q)x]^{1/(1-q)}$ is the function naturally emerging within nonextensive statistical mechanics. The entropic index is numerically given (at least for $alpha_A$ not too large) by $q = 1+(1/3) e^{-0.526 alpha_A}$, and the characteristic number of links by $kappa simeq 0.1+0.08 alpha_A$. The $alpha_A=0$ particular case belongs to the same universality class to which the Barabasi-Albert model belongs. In addition to this, we have numerically studied the rate at which the average number of links $<k_i>$ increases with the scaled time $t/i$; asymptotically, $<k_i > propto (t/i)^beta$, the exponent being close to $beta={1/2}(1-alpha_A)$ for $0 le alpha_A le 1$, and zero otherwise. The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs $Gamma$-space for Hamiltonian systems) a scale-free network.



قيم البحث

اقرأ أيضاً

We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by obeying a power law distribution.
341 - Yasuhiro Hashimoto 2015
In the Yule-Simon process, selection of words follows the preferential attachment mechanism, resulting in the power-law growth in the cumulative number of individual word occurrences. This is derived using mean-field approximation, assuming a continu um limit of both the time and number of word occurrences. However, time and word occurrences are inherently discrete in the process, and it is natural to assume that the cumulative number of word occurrences has a certain fluctuation around the average behavior predicted by the mean-field approximation. We derive the exact and approximate forms of the probability distribution of such fluctuation analytically and confirm that those probability distributions are well supported by the numerical experiments.
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation transition usin g a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities $p_k$. To illustrate the techniques and support our findings using Monte-Carlo simulations, we introduce the exemplary linking rule $p_k$ proportional to $k^{-alpha}$, with $alpha$ between -1 and plus infinity. This parameter may be used to interpolate between different regimes. For negative $alpha$, links are most likely attached to high-degree nodes. On the other hand, in case $alpha>0$, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.
We propose a two-parametric non-distributive algebraic structure that follows from $(q,q)$-logarithm and $(q,q)$-exponential functions. Properties of generalized $(q,q)$-operators are analyzed. We also generalize the proposal into a multi-parametric structure (generalization of logarithm and exponential functions and the corresponding algebraic operators). All $n$-parameter expressions recover $(n-1)$-generalization when the corresponding $q_nto1$. Nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures, in which this work is a consequence.
After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index $q_{mix} le 1$) and equilibration (characterized by the entropic index $q_{eq} ge 1$ ) play central and inter-related roles, and appear to determine {it a priori} the values of the relevant indices of the formalism. Boltzmann-Gibbs statistical mechanics is recovered as the $q_{mix}=q_{eq}=1$ particular case.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا