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1.
Zhongzhi Zhang Alafate Julaiti Baoyu Hou Hongjuan Zhang Guanrong Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,84(4):691-697
In this paper, by using two different techniques we derive an explicit formula for the
mean first-passage time (MFPT) between any pair of nodes on a general undirected network,
which is expressed in terms of eigenvalues and eigenvectors of an associated matrix
similar to the transition matrix. We then apply the formula to derive a lower bound for
the MFPT to arrive at a given node with the starting point chosen from the stationary
distribution over the set of nodes. We show that for a correlated scale-free network of
size N with a degree distribution
P(d) ∼ d
−γ
,
the scaling of the lower bound is
N
1−1/γ
. Also, we
provide a simple derivation for an eigentime identity. Our work leads to a comprehensive
understanding of recent results about random walks on complex networks, especially on
scale-free networks. 相似文献
2.
Controlling the noise enhanced stability effect via noise recycling in a metastable system 总被引:1,自引:0,他引:1
Z. L. Jia D. C. Mei 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(4):139
We analyze the role of the delay time τ
d
and the fraction ε of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated
by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that
MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of
the noise enhanced stability (NES) phenomenon. The increasing of τ
d
or ε strengthens the NES effect for ε > 0. However, for ε < 0, there is a critical value of τ
d
, below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends
to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ
d
or |ε| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the
noise recycling may be used as an effective scheme for controlling the NES effect. 相似文献
3.
Recently a great deal of effort has been made to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs of nodes on a fractal network. In this paper, we first propose a family of generalized delayed recursive trees characterized by two parameters, where the existing nodes have a time delay to produce new nodes. We then study the MFPT of random walks on this kind of recursive tree and investigate the effect of the time delay on the MFPT. By relating random walks to electrical networks, we obtain an exact formula for the MFPT and verify it by numerical calculations. Based on the obtained results, we further show that the MFPT of delayed recursive trees is much shorter, implying that the efficiency of random walks is much higher compared with the non-delayed counterpart. Our study provides a deeper understanding of random walks on delayed fractal networks. 相似文献
4.
Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises
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For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time (MFPT) and the spectral power amplification (SPA) are obtained, respectively. Based on the numerical computations, it is found that: (i) The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises (λ>0), this maximum for MFPT shows the characteristic of the entropic noise induced stability (ENIS) effect. The intensity λ of correlations between two noises can enhance the ENIS effect. (ii) The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon. 相似文献
5.
Zhongzhi Zhang Shuyang Gao 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,80(2):209-216
Random walks on complex networks, especially scale-free
networks, have attracted considerable interest in the past few
years. A lot of previous work showed that the average receiving time
(ART), i.e., the average of mean first-passage time (MFPT) for
random walks to a given hub node (node with maximum degree) averaged
over all starting points in scale-free small-world networks exhibits
a sublinear or linear dependence on network order N (number of
nodes), which indicates that hub nodes are very efficient in
receiving information if one looks upon the random walker as an
information messenger. Thus far, the efficiency of a hub node
sending information on scale-free small-world networks has not been
addressed yet. In this paper, we study random walks on the class of
Koch networks with scale-free behavior and small-world effect. We
derive some basic properties for random walks on the Koch network
family, based on which we calculate analytically the average sending
time (AST) defined as the average of MFPTs from a hub node to all
other nodes, excluding the hub itself. The obtained closed-form
expression displays that in large networks the AST grows with
network order as N ln N, which is larger than the linear scaling
of ART to the hub from other nodes. On the other hand, we also
address the case with the information sender distributed uniformly
among the Koch networks, and derive analytically the global mean
first-passage time, namely, the average of MFPTs between all couples
of nodes, the leading scaling of which is identical to that of AST.
From the obtained results, we present that although hub nodes are
more efficient for receiving information than other nodes, they
display a qualitatively similar speed for sending information as
non-hub nodes. Moreover, we show that that AST from a starting point
(sender) to all possible targets is not sensitively affected by the
sender’s location. The present findings are helpful for better
understanding random walks performed on scale-free small-world
networks. 相似文献
6.
Random walks on complex networks 总被引:3,自引:0,他引:3
We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction. 相似文献
7.
8.
Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap
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In this paper,we study the scaling for the mean first-passage time(MFPT) of the random walks on a generalized Koch network with a trap.Through the network construction,where the initial state is transformed from a triangle to a polygon,we obtain the exact scaling for the MFPT.We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order.In addition,we determine the exponents of scaling efficiency characterizing the random walks.Our results are the generalizations of those derived for the Koch network,which shed light on the analysis of random walks over various fractal networks. 相似文献
9.
In this paper, we investigate a mathematical model for describing the growth of tumor cell under immune response, which is
driven by cross-correlation between multiplicative and additive colored noises as well as the nonzero cross-correlation in
between. The expression of the mean first-passage time (MFPT) is obtained by virtue of the steepest-descent approximation.
It is found: (i) When the noises are negatively cross-correlated (λ<0), then the escape is faster than in the case with no correlation (λ=0); when the noises are positively cross-correlated (λ>0), then the escape is slower than in the case with no correlation. Moreover, in the case of positive cross-correlation,
the escape time has a maximum for a certain intensity of one of the noises, i.e., the maximum for MFPT identifies the noise
enhanced stability of the cancer state. (ii) The effect of the cross-correlation time τ
3 on the MFPT is completely opposite for λ>0 and λ<0. (iii) The self-correlation times τ
1 and τ
2 of colored noises can enhance stability of the cancer state, while the immune rate β can reduce it. 相似文献
10.
Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap
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In this paper, we study the scaling for the mean first-passage time (MFPT) of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks. 相似文献
11.
12.
We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment μ = qd fixed. We discuss our results on the basis of the first- and second-rank orientational order parameters, angular distribution functions, chain-length distributions, and snapshots. At a low density, we have found chain formation with longer chains as the distance d is increased. At a high density, we have found phase transition from an orientationally ordered ferroelectric nematic phase (at low d) into an isotropic liquid containing chains (at large d). 相似文献
13.
S. Blügel B. Drittler R. Zeller P. H. Dederichs 《Applied Physics A: Materials Science & Processing》1989,49(6):547-562
We report results of systematic calculations for magnetic properties of 3d transition metal monolayers on Pd(001) and Ag(001). We find large similarities to interactions of magnetic 3d impurities in the bulk. Therefore the overlayer results are supplemented with results for 3d dimers in Cu, Ag, and Pd. Differences between the two classes of systems are utilized to reveal the interaction within the overlayers and between overlayers and substrates. In virtually all cases we find both ferromagnetic and antiferromagnetic solutions, showing large magnetic moments and similar densities of states. From the trend of the calculations we conclude that V, Cr, and Mn overlayers favor the antiferromagnetic c(2×2) structure, while Ti, Fe, Co, and Ni prefer the ferromagnetic one. 相似文献
14.
D. Chruściński A. Rutkowski 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,62(2):273-277
We provide a new class of entanglement witnesses for d ⊗ d systems (two qudits). Our construction generalizes the one proposed recently by Jafarizadeh et al. for d = 3 and d = 4 on the basis of semidefinite linear programming. Moreover, we provide a new class of PPT entangled states detected by
our witnesses which generalizes well known family of states constructed by Horodecki et al. for d = 3. 相似文献
15.
Many cytoskeletal biopolymers are "active," consuming energy in large quantities. In this Letter, we identify a fundamental difference between active polymers and passive, equilibrium polymers: for equal mean lengths, active polymers can reorganize faster than equilibrium polymers. We show that equilibrium polymers are intrinsically limited to linear scaling between mean lifetime (or mean first-passage time, or MFPT) and mean length, MFPT~, by analogy to 1D Potts models. By contrast, we present a simple active-polymer model that improves upon this scaling, such that MFPT~(1/2). Since, to be biologically useful, structural biopolymers must typically be many monomers long yet respond dynamically to the needs of the cell, the difference in reorganization kinetics may help to justify the active polymers' greater energy cost. 相似文献
16.
Bao-quan Ai Hua Zheng Xue-rong Zhang Ning-xing Wang Liang-gang Liu 《International Journal of Theoretical Physics》2006,45(11):2143-2149
The transient properties of a bistable system with the stochastic potentials are investigated. The explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The results show that the MFPT of the system increases with the amplitude Δ of the stochastic potential, decreases with the noise intensity D and the correlation length l. The stochastic potential makes against the particle moving towards the destination. 相似文献
17.
Previous work shows that the mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) in uncorrelated random scale-free networks is closely related to the exponent γ of power-law degree distribution P(k) ~ k(-γ), which describes the extent of heterogeneity of scale-free network structure. However, extensive empirical research indicates that real networked systems also display ubiquitous degree correlations. In this paper, we address the trapping issue on the Koch networks, which is a special random walk with one trap fixed at a hub node. The Koch networks are power-law with the characteristic exponent γ in the range between 2 and 3, they are either assortative or disassortative. We calculate exactly the MFPT that is the average of first-passage time from all other nodes to the trap. The obtained explicit solution shows that in large networks the MFPT varies lineally with node number N, which is obviously independent of γ and is sharp contrast to the scaling behavior of MFPT observed for uncorrelated random scale-free networks, where γ influences qualitatively the MFPT of trapping problem. 相似文献
18.
We study the largest Liapunov exponent for products of random matrices. The two classes of matrices considered are discrete,d-dimensional Laplacians, with random entries, and symplectic matrices that arise in the study ofd-dimensional lattices of coupled, nonlinear oscillators. We derive bounds on this exponent for all dimensions,d, and we show that ifd3, and the randomness is not too strong, one can obtain an explicit formula for the largest exponent in the thermodynamic limit. Our method is based on an equivalence between this problem and the problem of directed polymers in a random environment. 相似文献
19.
Noam Berger 《Communications in Mathematical Physics》2002,226(3):531-558
We study the behavior of the random walk on the infinite cluster of independent long-range percolation in dimensions d= 1,2, where x and y are connected with probability . We show that if d<s<2d, then the walk is transient, and if s≥ 2d, then the walk is recurrent. The proof of transience is based on a renormalization argument. As a corollary of this renormalization
argument, we get that for every dimension d≥ 1, if d>s>2d, then there is no infinite cluster at criticality. This result is extended to the free random cluster model. A second corollary
is that when d≥& 2 and d>s>2d we can erase all long enough bonds and still have an infinite cluster. The proof of recurrence in two dimensions is based
on general stability
results for recurrence in random electrical networks. In particular, we show that i.i.d. conductances on a recurrent graph
of bounded degree yield a recurrent electrical network.
Received: 27 October 2000 / Accepted: 29 November 2001 相似文献
20.
G.G.N. Angilella A. Sudbø R. Pucci 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(2):269-275
Remarkable anisotropic structures have been recently observed in the order parameter of the underdoped superconductor Bi2Sr2CaCu2O . Such findings are strongly suggestive of deviations from a simple d
x2 - y2
-wave picture of high- superconductivity, i.e.
. In particular, flatter nodes in are observed along the directions in -space, than within this simple model for a d-wave gap. We argue that nonlinear corrections in the -dependence of near the nodes introduce new energy scales, which would lead to deviations in the predicted power-law asymptotic behaviour
of several measurable quantities, at low or intermediate temperatures. We evaluate such deviations, either analytically or
numerically, within the interlayer pair-tunneling model, and within yet another phenomenological model for a d-wave order parameter. We find that such deviations are expected to be of different sign in the two cases. Moreover, the doping
dependence of the flatness of the gap near the nodes is also attributable to Fermi surface effects, in addition to possible
screening effects modifying the in-plane pairing kernel, as recently proposed.
Received 19 November 1999 相似文献