共查询到20条相似文献,搜索用时 531 毫秒
1.
F. Pammolli D. Fu S. V. Buldyrev M. Riccaboni K. Matia K. Yamasaki H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(2):127-130
We introduce a model of proportional growth to explain the distribution P(g) of business firm growth rates. The model predicts
that P(g) is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3.
Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body
of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries,
and we find that the predictions are in good agreement with empirical evidence on both growth distributions and size-variance
relationships. 相似文献
2.
We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. There are three well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide exact results on the distributions which are not known yet for binary interactions. Our model easily reproduces the power law for the size distribution of firms (Zipf’s law). The fluctuations in the growth rate falls with increasing size following a power law (though the exponent does not match with the data). However, the distribution of the difference of the firm size in this model has Laplace distribution whereas the real data suggests that the difference of the log of sizes has the same distribution. 相似文献
3.
We present a growth model for a system of cities. This model recovers not only Zipf's law but also other kinds of city size distributions (CSDs). A new positive exponent α, which yields Zipf's law only when equal to 1, was introduced. We define three classes of CSD depending on the value of α: larger than, smaller than, or equal to 1. The model is based on a random growth of the city population together with the variation of the number of cities in the system. The striking result is the peculiar behavior of the model: it is only statistical deterministic. Moreover, we found that the exponent α may be larger, smaller or equal to 1, just like in real systems of cities, depending on the rate of creation of new cities and the time elapsed during the growth. It is to our knowledge the first time that the influence of the time on the type of the distribution is investigated. The results of the model are in very good agreement with real CSD. The classification and model can be also applied to other entities like countries, incomes, firms, etc 相似文献
4.
D.F. Zheng P.M. Hui K.F. Yip N.F. Johnson 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(2):213-218
We present generalized dynamical models describing the sharing of information, and the corresponding herd behavior, in a population
based on the recent model proposed by Eguıluz and Zimmermann (EZ) [Phys. Rev. Lett. 85, 5659 (2000)]. The EZ model, which is a dynamical version of the herd formation model of Cont and Bouchaud (CB), gives a
reasonable model for the formation of clusters of agents and for actions taken by clusters of agents. Both the EZ and CB models
give a cluster size distribution characterized by a power law with an exponent -5/2. By introducing a size-dependent probability
for dissociation of a cluster of agents, we show that the exponent characterizing the cluster size distribution becomes model-dependent
and non-universal, with an exponential cutoff for large cluster sizes. The actions taken by the clusters of agents generate
the price returns, the distribution of which is also characterized by a model-dependent exponent. When a size-dependent transaction
rate is introduced instead of a size-dependent dissociation rate, it is found that the distribution of price returns is characterized
by a model-dependent exponent while the exponent for the cluster-size distribution remains unchanged. The resulting systems
provide simplified models of a financial market and yield power law behaviour with an easily tunable exponent.
Received 31 December 2001 相似文献
5.
In the business firm network, the number of in-degrees and out-degrees show the same scale-free property, however, the distribution of authorities and hubs show asymmetric behavior. Here we show the result of an analysis of the two-link structure of the network to find the origin of this asymmetric behavior. We find the tendency for big construction firms intermediating small subcontracting firms to have higher hub degrees. By measuring the strength of preferential attachment rate of new companies, we also find a abnormally strong preferential attachment for which the exponent is 1.4 with respect to out-degree when a new company forms a business partnership with a construction company. We propose a new model that reproduces the asymmetric behavior of the degrees of authorities and hubs by changing the preferential attachment rate between the in-degree and the out-degree in the business firm network. 相似文献
6.
A. Sarkar P. Ghosh S. K. Chattopadhyay A. K. Meikap A. Bhattacharyay S. K. Chatterjee G. C. Das S. Mukherjee M. K. Mitra 《Czechoslovak Journal of Physics》2006,56(2):201-210
The low frequency (20 Hz to 1 MHz) ac conductivity and magnetoconductivity behaviour of ceramic nanocomposite (Ni-SiO2) at low temperature down to 77 K are reported. The frequency dependent conductivity followed the power law, σ(ω) ∝ ω
s
. The fractional exponent s is a function of temperature and was found to increase with increasing temperature. This type of variation may be attributed
to small polaron hopping. A peak present in the loss tangent indicates the presence of a Debye relaxation process. The magnetoconductivity
of the samples is positive, which strongly depends on frequency. A firm theoretical explanation of frequency dependent magnetoconductivity
is still lacking. 相似文献
7.
Chen SH Liao C Sciortino F Gallo P Tartaglia P 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,59(6):6708-6714
We analyze a set of 10 M-step molecular dynamics (MD) data of low-temperature SPC/E model water with a phenomenological analytical model. The motivation is twofold: to extract various k-dependent physical parameters associated with the single-particle or the self-intermediate scattering functions (SISFs) of water at a deeply supercooled temperature and to apply this analytical model to analyses of new high resolution quasielastic neutron scattering data presented elsewhere. The SISF of the center of mass computed from the MD data show clearly time-separated two-step relaxations with a well defined plateau in between. We model the short time relaxation of the test particle as a particle trapped in a harmonical potential well with the vibrational frequency distribution function having a two-peak structure known from previous inelastic neutron scattering experiments. For the long time part of the relaxation, we take the alpha relaxation suggested by mode-coupling theory. The model fits the low-temperature SISF over the entire time range from 1 fs to 10 ns, allowing us to extract peak positions of the vibrational density of states, the structural relaxation rate 1/tau of the cage (the potential well) and the stretch exponent beta. The structural relaxation rate has a power law dependence on the magnitude of the wave vector transfer k and the stretch exponent varies from 0.55 at large k to unity at small k. 相似文献
8.
F. Semboloni 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(3):295-301
We show that a hierarchical cities structure can be generated by a self-organized process which grows with a bottom-up mechanism,
and that the resulting distribution is power law. First we
analytically prove that the power law distribution satisfies the balance between the offer of the city and the demand of its
basin of attraction, and that the exponent in the Zipf's law corresponds to the multiplier linking the population of the central
city to the population of its basin of attraction. Moreover, the corresponding hierarchical structure shows a variable
spanning factor, and the population of the cities linked
to the same city up in the hierarchy is variable as well. Second a stochastic
dynamic spatial model is proposed, whose numerical results confirm the analytical
findings. In this model, inhabitants minimize the transportation cost, so that the greater
the importance of this cost, the more stable is the system in its microscopic aspect.
After a comparison with the existent methods for the generation of a
power law distribution, conclusions are drawn on the connection of hierarchical
structure, and power law distribution, with the functioning of the system of cities. 相似文献
9.
M. Bologna H. Calisto 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,83(3):409-414
In this paper we consider a general growth model with stochastic growth rate modelled via
a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its
probability distribution. We consider the, as yet, unexplored case where the deterministic
growth rate is perturbed by a dichotomic noise characterized by a waiting time
distribution in the two state that is a power law with
power 1 <
μ
< 2. We
apply the results to two well-known growth models; Malthus-Verhulst and Gompertz. 相似文献
10.
The Zipf’s law is studied here in the context of size distribution of Indian cities and the power law exponent is estimated.
We have used the data from the Indian censuses of 1981,1991 and 2001. The analysis shows that the population distribution
in Indian cities do follow a power law similar to the ones found in other countries. The scaling exponent are found to be
2.15 ± 0.01 for 1981, 2.11 ± 0.01 for 1991 and 2.05 ± 0.02 for 2001 from the linear fit. We have also estimated the scaling
exponent from the maximum likelihood estimator technique which is found to be 2.04 ±.07 for the year 2001. 相似文献
11.
We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguíluz and Zimmermann. A characteristic size of group of agents s0 is introduced. The fragmentation and coagulation rates of groups of agents are assumed to depend on the size of the group. We present results of numerical simulations and mean field analysis. It is found that the size distribution of groups of agents ns exhibits two distinct scaling behavior depending on ss0 or s>s0. For ss0, nss−(5/2+δ), while for s>s0,nss−(5/2−δ), where δ is a model parameter representing the sensitivity of the fragmentation and coagulation rates to the size of the group. Our model thus gives a tunable exponent for the size distribution together with two scaling regimes separated by a characteristic size s0. Suitably interpreted, our model can be used to represent the formation of groups of customers for certain products produced by manufacturers. This, in turn, leads to a distribution in the size of businesses. The characteristic size s0, in this context, represents the size of a business for which the customer group becomes too large to be kept happy but too small for the business to become a brand name. 相似文献
12.
A discretized version of the Burridge-Knopoff train model with (non-linear friction force replaced by) random pinning is studied in one and two dimensions. A scale free distribution of avalanches and the Omori law type behaviour for after-shocks are obtained. The avalanche dynamics of this model becomes precisely similar (identical exponent values) to the Edwards-Wilkinson (EW) model of interface propagation. It also allows the complimentary observation of depinning velocity growth (with exponent value identical with that for EW model) in this train model and Omori law behaviour of after-shock (depinning) avalanches in the EW model. 相似文献
13.
Kinetic equations with relaxation collision kernels are considered under the basic assumption of two collision invariants,
namely mass and energy. The collision kernels are of BGK-type with a general local Gibbs state, which may be quite different
from the Gaussian. By the use of the diffusive length/time scales, energy transport systems consisting of two parabolic equations
with the position density and the energy density as unknowns are derived on a formal level. The H theorem for the kinetic
model is presented, and the entropy for the energy transport systems, which is inherited from the kinetic model, is derived.
The energy transport systems for specific examples of the global Gibbs state, such as a power law with negative exponent,
a cut-off power law with positive exponent, the Maxwellian, Bose–Einstein, and Fermi–Dirac distributions, arepresented.
MSC classification (2000): Primary: 82C40, 35B40; Secondary: 35K55, 45K05, 82D05, 85A05x 相似文献
14.
D. Helbing B. Tilch 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(4):577-586
We study the duration of “high-flow states” in freeway traffic, defined as the time periods for which traffic flows exceed
a given flow threshold. Our empirical data are surprisingly well represented by a power law. Moreover, the power law exponent
for a two-lane freeway seems to be independent of the chosen flow threshold. In order to interpret this discovery, we investigate
a simple theoretical model of heterogeneous traffic with overtaking maneuvers, which is able to reproduce both, the empirical
power law and its exponent. 相似文献
15.
G.-F. Gu W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(4):585-592
Recently, Mike and Farmer have constructed a very powerful
and realistic behavioral model to mimick the dynamic process of
stock price formation based on the empirical regularities of order
placement and cancelation in a purely order-driven market, which can
successfully reproduce the whole distribution of returns, not only
the well-known power-law tails, together with several other
important stylized facts. There are three key ingredients in the
Mike-Farmer (MF) model: the long memory of order signs characterized
by the Hurst index Hs, the distribution of relative order prices
x in reference to the same best price described by a Student
distribution (or Tsallis’ q-Gaussian), and the dynamics of order
cancelation. They showed that different values of the Hurst index
Hs and the freedom degree αx of the Student distribution
can always produce power-law tails in the return distribution
fr(r) with different tail exponent αr. In this paper, we
study the origin of the power-law tails of the return distribution
fr(r) in the MF model, based on extensive simulations with
different combinations of the left part L(x) for x < 0 and the
right part R(x) for x > 0 of fx(x). We find that power-law
tails appear only when L(x) has a power-law tail, no matter R(x)
has a power-law tail or not. In addition, we find that the
distributions of returns in the MF model at different timescales can
be well modeled by the Student distributions, whose tail exponents
are close to the well-known cubic law and increase with the
timescale. 相似文献
16.
We study experimentally the slow growth of a single crack in a fibrous material and observe stepwise growth dynamics. We model the material as a lattice where the crack is pinned by elastic traps and grows due to thermally activated stress fluctuations. In agreement with experimental data we find that the distribution of step sizes follows subcritical point statistics with a power law (exponent 3/2) and a stress-dependent exponential cutoff diverging at the critical rupture threshold. 相似文献
17.
Sander?Dommers Cristian?Giardinà Remco?van?der?Hofstad 《Journal of statistical physics》2010,141(4):638-660
We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit
of the pressure when the mean degree is finite (degree exponent τ>2), for which the random graph has a tree-like structure. For this, we closely follow the analysis by Dembo and Montanari
(Ann. Appl. Probab. 20(2):565–592, 2010) which assumes finite variance degrees (τ>3), adapting it when necessary and also simplifying it when possible. Our results also apply in cases where the degree distribution
does not obey a power law. 相似文献
18.
N. J. Moura M. B. Ribeiro 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(1):101-120
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available
from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for
99% of the economically less favorable population is well represented by a Gompertz curve of the form G(x) = exp [exp (A-Bx)],
where x is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of
the population is well represented by a Pareto power law distribution P(x) = βx-α. This result means that similarly to other countries, Brazil’s income distribution is characterized by a well defined two
class system. The parameters A, B, α, β were determined by a mixture of boundary conditions, normalization and fitting methods
for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here
suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic
system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the
total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each
component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil’s economic system might
possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth
and cycle. 相似文献
19.
Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered an important property of these systems. In general, power law exists in the central part of the distribution. It has deviations from power law for very small and very large variable sizes. Tsallis, through non-extensive thermodynamics, explained power law distribution in many cases including deviation from the power law. In case of very large steps, they used the heuristic crossover approach. In the present work, we present an alternative model in which we consider that the entropy factor q decreases with variable size due to the softening of long range interactions or memory. We apply this model for distribution of citation index of scientists and examination scores and are able to explain the distribution for entire variable range. In the present model, we can have very sharp cut-off without interfering with power law in its central part as observed in many cases. 相似文献
20.
A model, introduced earlier for the dynamics of a
generic efficiency measure in a population of agents by Majumdar
and Krapivsky (Phys. Rev. E 63, 054101 (2001)), is investigated on
scale-free networks whose degree distribution follows a power law
with the tunable exponent γ. The model shows a
delocalization transition from a stagnant phase to a growing one
when decreasing the degree exponent γ of scale-free
networks. By taking into account the specific dynamical properties
of the model and the geometrical properties of scale-free
networks, we predict the appearance of this critical transition.
This work is useful for understanding these kinds of transitions
occurring in many dynamical processes on scale-free networks. 相似文献