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1.
The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative
coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method,
the analytic expressions of the stationary probability distribution Pst(x), the relaxation time Tc, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation
strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation
strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation
time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time
τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time Tc is a stochastic resonant phenomenon, and distribution
curves exhibit a single-maximum structure. 相似文献
2.
3.
我们在Oregonator模型的基础上,取速率常数k6、理想配比系数f及波数k为参变量,首先讨论了B-Z反应体系的稳定性,并得到了下列各量的表达式:空间周期结构的临界速率常数k6c、短波临界波数ksc与长波临界波数kLc,时空周期结构的临界速率常数k6c及临界波数kc等。而后,我们给出了B-Z反应体系的临界频率λc,讨论了体系在临界状态附近的行为,并得到了触发波速度uT及相位波速度uP的表达式。本文的结论是,在一定条件下,不搅拌的B-Z反应体系能在临界状态附近呈现稳定的波群或者波包,触发波是均匀体系中的波包,相位波是有微小梯度的非均匀体系中的波包。uT=2ηDkc,D为HBrO2的扩散系数,η为[H+]的缓变函数(在实验观测范围内,η≈0.1);uP=v,v为相速度。
关键词: 相似文献
4.
We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark–gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent. 相似文献
5.
C. Monthus T. Garel 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(1):39-45
The directed polymer in a 1+3 dimensional
random medium is known to present a disorder-induced phase
transition. For a polymer of length L, the high temperature
phase is characterized by a diffusive behavior for the end-point
displacement R2 ∼L and by free-energy fluctuations of order
ΔF(L) ∼O(1). The low-temperature phase is characterized by
an anomalous wandering exponent R2/L ∼Lω and
by free-energy fluctuations of order ΔF(L) ∼Lω
where ω∼0.18. In this paper, we first study the scaling
behavior of various properties to localize the critical temperature
Tc. Our results concerning R2/L and ΔF(L) point towards
0.76 < Tc ≤T2=0.79, so our conclusion is that Tc is equal
or very close to the upper bound T2 derived by Derrida and
coworkers (T2 corresponds to the temperature above which the ratio
remains finite as L ↦
∞). We then present histograms for the free-energy, energy and
entropy over disorder samples. For T ≫Tc, the free-energy
distribution is found to be Gaussian. For T ≪Tc, the free-energy
distribution coincides with the ground state energy distribution, in
agreement with the zero-temperature fixed point picture. Moreover the
entropy fluctuations are of order ΔS ∼L1/2 and follow a
Gaussian distribution, in agreement with the droplet predictions,
where the free-energy term ΔF ∼Lω is a near
cancellation of energy and entropy contributions of order L1/2. 相似文献
6.
J.M. Drouffe C. Godrèche 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(2):281-288
We study the statistical properties of the sum S
t =
dt'σ
t', that is the difference of time spent positive or negative by the spin σ
t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution
of St and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature
( T > T
c), criticality ( T = T
c), and low temperature ( T < T
c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S
t/t was always larger than the equilibrium magnetization is found to decay as t
-
- ?. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase
of the three-dimensional Ising model.
Received 4 December 2000 相似文献
7.
Babu S Rottereau M Nicolai T Gimel JC Durand D 《The European physical journal. E, Soft matter》2006,19(2):203-211
Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid
bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles
(te). te is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion
of the particles. In the flocculation regime the fractal dimension of the clusters is df=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of te transient gels are formed. Close to the
percolation threshold the clusters have a fractal dimension df=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation
occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction. 相似文献
8.
We investigated numerically localization properties of electron eigenstates in a chain with long-range correlated diagonal
disorder. A tight-binding one-dimensional model with
on-site energies exhibiting long-range correlated disorder (LCD)
was used with various disorder strength W. LCD was defined so
that it gave a power-law spectral density of the form S(k)αk-p, where p determines the roughness of the potential landscape. Numerical results on the correlation length ξ of
eigenstates shows the existence of the localization-delocalization transition at p=2. It is found that the critical values
for disorder strength Wc and also the critical exponent ν for
localization length change with the values of p. 相似文献
9.
R. M. D'Souza P. L. Krapivsky C. Moore 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(4):535-543
The “power of choice” has been shown to radically alter the behavior of a number of
randomized algorithms. Here we explore the effects of choice on models of random tree growth.
In our models each new node has k randomly chosen contacts, where k > 1 is a constant.
It then attaches to whichever one of these contacts is most desirable in some sense, such as its
distance from the root or its degree. Even when the new node has just two choices,
i.e., when k = 2, the resulting tree can be very different from a random graph or tree. For instance,
if the new node attaches to the contact which is closest to the root of the tree, the
distribution of depths changes from Poisson to a traveling wave solution.
If the new node attaches to the contact with the smallest degree, the degree distribution
is closer to uniform than in a random graph, so that with high probability there are no nodes in the
tree with degree greater than O(log log N). Finally, if the new node attaches to the contact
with the largest degree, we find that the degree distribution is a power law with exponent -1
up to degrees roughly equal to k, with an exponential cutoff beyond that; thus, in this case,
we need k ≫ 1 to see a power law over a wide range of degrees. 相似文献
10.
B. Zeini A. Freimuth B. Büchner M. Galffy R. Gross A.P. Kampf M. Kläser G. Müller-Vogt L. Winkler 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,20(2):189-208
Measurements of the thermal conductivity (kxx) and the thermal Hall effect (kxy) in high magnetic fields in Y- and Bi-based high-T
c
superconductors are presented. We describe the experimental technique and test measurements on a simple metal (niobium).
In the high-T
c
superconductors kxx and kxy increase below T
c
and show a maximum in their temperature dependence. kxx has contributions from phonons and quasiparticle (QP) excitations, whereas kxy is purely electronic. The strong increase of kxy below T
c
gives direct evidence for a strong enhancement of the QP contribution to the heat current and thus for a strong increase
of the QP mean free path. Using kxy and the magnetic field dependence of kxx we separate the electronic thermal conductivity ( k
xx
el
) of the CuO
2
-planes from the phononic thermal conductivity ( k
xx
ph
). In YBa2Cu3O
7 - δ
k
xx
el
shows a pronounced maximum in the superconducting state. This maximum is much weaker in Bi2Sr2CaCu2O
8 + δ
, due to stronger impurity scattering. The maximum of k
xx
el
is strongly suppressed by a magnetic field, which we attribute to the scattering of QPs on vortices. An additional magnetic
field independent contribution to the maximum of kxx occurs in YBa2Cu3O
7 - δ
, reminiscent of the contribution of the CuO-chains, as determined from the anisotropy in untwined single crystals. Our data analysis reveals that below T
c
as in the normal state a transport (τ) and a Hall (
) relaxation time must be distinguished: The inelastic (i.e. temperature dependent) contribution to τ is strongly enhanced in the superconducting state, whereas
displays the same temperature dependence as above T
c
. We determine also the electronic thermal conductivity in the normal state from kxy and the electrical Hall angle. It shows an unusual linear increase with temperature.
Received 23 August 2000 相似文献
11.
H. Hinrichsen M. Howard 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(4):635-643
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the
spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for
long-range infections which decays in d spatial dimensions as . Extensive numerical simulations are performed in order to determine the density exponent and the correlation length exponents and for various values of . We observe that these exponents vary continuously with , in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with
algebraically distributed long-range interactions.
Received: 4 September 1998 / Accepted: 22 September 1998 相似文献
12.
F.A.B.F. de Moura F. Domínguez-Adame 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(2):165-169
We study the nature of the vibrational modes in a two-dimensional harmonic
lattice with long-range correlated random masses, with power-law spectral
density S(k)∼1/kα. We obtain numerically the scale invariance of
the fluctuations of the relative participation number and the local density of
states. We find signatures of extended vibrational modes when α>αc
and αc depends on the magnitude of disorder. In order to confirm this
claim, we also study the time evolution of an initially localized perturbation
of the lattice. We show that the second moment of the spatial distribution of
the energy displays a ballistic regime when α>αc, in agreement with
the occurrence of extended vibrational modes. 相似文献
13.
L. Turban 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(3):331-338
Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation
threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio r
eff = ct/L
z, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour
of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for
isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture.
Received 10 February 2003 Published online 20 June 2003
RID="a"
ID="a"e-mail: turban@lpm.u-nancy.fr
RID="b"
ID="b"UMR CNRS 7556 相似文献
14.
D.A. Matoz-Fernandez 《Physica A》2008,387(26):6513-6525
Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length k (k-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel k-mers, is separated from the isotropic state, by a continuous transition occurring at a finite density θc. Our study allowed: (1) to determine the minimum value of k (kmin), which allows the formation of the nematic phase, being kmin=11; (2) to predict the dependence of θc on k, being θc(k)∝k−1; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class. 相似文献
15.
Lu CY Chen P Ishii Y Komura S Kato T 《The European physical journal. E, Soft matter》2008,25(1):91-101
We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C12E5 /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of
a lamellar or smectic phase is proposed with a prediction
∼ σ3/2 , where
is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the
main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is
estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the
shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further
flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent. 相似文献
16.
J.R. Fry P.R. Noble W.H. Evans A. Moreton G. Ekspong H. Gennow E. Johansson P. Lundborg S. Nilsson J. Norrby Y. Yamdagni H. Fenker J. Marraffino S. Reucroft C. Roos M. Webster 《Nuclear Physics B》1979,152(1):27-35
From an exposure of the 30-inch deuterium filled bubble chamber to a 100 GeV/c antiproton-enriched beam at FNAL, we have calculated the topological cross sections for antiproton-neutron interactions with three or more charged particles in the final state. A comparison of our data with pn data at the same momentum allows us to estimate the annihilation contribution to each multiplicity, and hence calculate the average value, and width, of the annihilation multiplicity distribution. Our results are consistent with those from data at 100 GeV/c, but depart from the trend of lower-energy data. 相似文献
17.
We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together
(ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement
with our previous work (Europhys. Lett.
73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k
ring(t) ∝ t
-δ and k
eq(t) ∝ t
1-δ for times less than the longest polymer relaxation time. Here δ is an effective exponent which approaches δ = 5/4 for very
long Rouse chains. Our present analysis also suggests a “sub-leading” term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics,
our RG analysis indicates that the leading time dependence for the reaction rate is k(t) ∼ 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial
conditions. We also find a logarithmic correction term which we “exponentiate” to a logarithmic form with a Landau pole. The
presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction
rate. 相似文献
18.
K.H. Lee 《Physica A》2008,387(26):6657-6662
Using the context of routing efficiency in a complex scale-free network, we study the problem of how a limited amount of resources should be distributed to the nodes in a network so as to achieve a better performance, without imposing a certain pre-determined distribution. A dynamical reallocation scheme, based on the willingness of sharing resources with a busy neighboring node, is proposed as a tool for allowing an initially uniform distribution of resource to evolve to a high-performance distribution. The resulting distribution gives a critical packet generation rate Rc that is significantly enhanced when compared with evenly distributing the same amount of resources on the nodes. There emerges a relation between the resource allocated to a node and the degree of the node in the form of . The exponent γ is found to vary with the packet generation rate R. For R<Rc, γ takes on a high value and shows a weak dependence on R; for R>Rc, γ drops with R; and for R?Rc, γ saturates. For good performance, the values of γ indicate a behavior different from that linear in k, as often assumed in previous studies. The resource distribution is also analyzed in terms of the betweenness of the nodes. 相似文献
19.
Time-dependent fluctuations in a system of coagulating particles are studied, using the master equation for the probability distributionsP(m,t) for the occupation numbersm={m
k} (k=1,2,...) of thek-cluster states. Van Kampen's-expansion is used to determine the deterministic (order
0) and fluctuating part (order
–1/2) of the solution. We calculate the time-dependent behavior of the fluctuations in the cluster size distribution. The model under consideration is of special interest since it exhibits a phase transition (gelation). For monodisperse initial states we give explicit expressions for the probability distribution of the fluctuations and for the equal-time and two-time correlation functions also near the phase transition. For general initial conditions we study the fluctuations (1) for large cluster sizes, (2) in the scaling limit (near the critical point), and (3) for large times. Our results show that the deterministic approach to coagulation processes (Smoluchowski theory) is invalid very close to the gelpointt
c and at large times (tt
M), where the distance from the gelpoint and the timet
M depend upon the size of the system. 相似文献
20.
E. Bertin P. Bonville J.-P. Bouchaud J.A. Hodges J.P. Sanchez P. Vulliet 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):347-354
Using 155Gd M?ssbauer spectroscopy down to 27 mK, we show that, in the geometrically frustrated pyrochlore Gd2Sn2O7, the Gd3+ hyperfine levels are populated out of equilibrium. From this, we deduce that the hyperfine field, and the correlated Gd3+ moments which produce this field, continue to fluctuate as T
↦ 0. With a model of a spin 1/2 system experiencing a magnetic field which reverses randomly in time, we obtain an analytical
expression for the steady state probability distribution of the level populations. This distribution is a simple function
of the ratio of the nuclear spin relaxation time to the average electronic spin-flip time. In Gd2Sn2O7, we find the two time scales are of the same order of magnitude. We discuss the mechanism giving rise to the nuclear spin
relaxation and the influence of the electronic spin fluctuations on the hyperfine specific heat. The corresponding low temperature
measurements in Gd2Ti2O7 are presented and discussed.
Received 17 October 2001 Published online 6 June 2002 相似文献