اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAverage Trapping time on the 3-dimensional 3-level Sierpinski gasket network with a set of trap nodes
155
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
As a basic dynamic feature on complex networks, the property of random walk has received a lot of attention in recent years. In this paper, we first studied the analytical expression of the mean global first passage time (MGFPT) on the 3-dimensional 3-level Sierpinski gasket network. Based on the self-similar structure of the network, the correlation between the MGFPT and the average trapping time (ATT) is found, and then the analytical expression of the ATT is obtained. Finally, by establishing a joint network model, we further give the standard process of solving the analytical expression of the ATT when there is a set of trap nodes in the network. By illustrating examples and numerical simulations, it can be proved that when the trap node sets are different, the ATT will be quite different, but the the super-linear relationship with the number of iterations will not be changed.
قيم البحث
اقرأ أيضاً
As a classic self-similar network model, Sierpinski gasket network has been used many times to study the characteristics of self-similar structure and its influence on the dynamic properties of the network. However, the network models studied in thes
e problems only contain a single self-similar structure, which is inconsistent with the structural characteristics of the actual network models. In this paper, a type of horizontally segmented 3 dimensional Sierpinski gasket network is constructed, whose main feature is that it contains the locally self-similar structures of the 2 dimensional Sierpinski gasket network and the 3 dimensional Sierpinski gasket network at the same time, and the scale transformation between the two kinds of self-similar structures can be controlled by adjusting the crosscutting coefficient. The analytical expression of the average trapping time on the network model is solved, which used to analyze the effect of two types of self-similar structures on the properties of random walks. Finally, we conclude that the dominant self-similar structure will exert a greater influence on the random walk process on the network.
We derive exactly the number of Hamiltonian paths H(n) on the two dimensional Sierpinski gasket SG(n) at stage $n$, whose asymptotic behavior is given by $frac{sqrt{3}(2sqrt{3})^{3^{n-1}}}{3} times (frac{5^2 times 7^2 times 17^2}{2^{12} times 3^5 tim
es 13})(16)^n$. We also obtain the number of Hamiltonian paths with one end at a certain outmost vertex of SG(n), with asymptotic behavior $frac {sqrt{3}(2sqrt{3})^{3^{n-1}}}{3} times (frac {7 times 17}{2^4 times 3^3})4^n$. The distribution of Hamiltonian paths on SG(n) with one end at a certain outmost vertex and the other end at an arbitrary vertex of SG(n) is investigated. We rigorously prove that the exponent for the mean $ell$ displacement between the two end vertices of such Hamiltonian paths on SG(n) is $ell log 2 / log 3$ for $ell>0$.
In the case of some fractals, sampling with average values on cells is more natural than sampling on points. In this paper we investigate this method of sampling on $SG$ and $SG_{3}$. In the former, we show that the cell graph approximations have the
spectral decimation property and prove an analog of the Shannon sampling theorem.. We also investigate the numerical properties of these sampling functions and make conjectures which allow us to look at sampling on infinite blowups of $SG$. In the case of $SG_{3}$, we show that the cell graphs have the spectral decimation property, but show that it is not useful for proving an analogous sampling theorem.
The multifractal behavior of the normalized first passage time is investigated on the two dimensional Sierpinski gasket with both absorbing and reflecting barriers. The normalized first passage time for Sinai model and the logistic model to arrive at
the absorbing barrier after starting from an arbitrary site, especially obtained by the calculation via the Monte Carlo simulation, is discussed numerically. The generalized dimension and the spectrum are also estimated from the distribution of the normalized first passage time, and compared with the results on the finitely square lattice.
We present the numbers of ice model and eight-vertex model configurations (with Boltzmann factors equal to one), I(n) and E(n) respectively, on the two-dimensional Sierpinski gasket SG(n) at stage $n$. For the eight-vertex model, the number of config
urations is $E(n)=2^{3(3^n+1)/2}$ and the entropy per site, defined as $lim_{v to infty} ln E(n)/v$ where $v$ is the number of vertices on SG(n), is exactly equal to $ln 2$. For the ice model, the upper and lower bounds for the entropy per site $lim_{v to infty} ln I(n)/v$ are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accurate. The corresponding result of ice model on the generalized two-dimensional Sierpinski gasket SG_b(n) with $b=3$ is also obtained. For the generalized vertex model on SG_3(n), the number of configurations is $2^{(8 times 6^n +7)/5}$ and the entropy per site is equal to $frac87 ln 2$. The general upper and lower bounds for the entropy per site for arbitrary $b$ are conjectured.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
