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1.
We have investigated the proof of the H theorem within a
manifestly covariant approach by considering the relativistic
statistical theory developed in [G. Kaniadakis, Phys. Rev. E 66, 056125 (2002); G. Kaniadakis, Phys. Rev. E 72, 036108 (2005)]. As it
happens in the nonrelativistic limit, the molecular chaos hypothesis
is slightly extended within the Kaniadakis formalism. It is shown
that the collisional equilibrium states (null entropy source term)
are described by a κ power law generalization of the
exponential Juttner distribution, e.g.,
,
with θ=α(x)+βμpμ, where α(x) is a
scalar, βμ is a four-vector, and pμ is the
four-momentum. As a simple example, we calculate the relativistic
κ power law for a dilute charged gas under the action of an
electromagnetic field Fμν. All standard results are readly
recovered in the particular limit κ→0. 相似文献
2.
Complexity of two-dimensional patterns 总被引:1,自引:0,他引:1
Yu.A. Andrienko N.V. Brilliantov J. Kurths 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(3):539-546
To describe quantitatively the complexity of two-dimensional patterns we introduce a complexity measure based on a mean information
gain. Two types of patterns are studied: geometric ornaments and patterns arising in random sequential adsorption of discs
on a plane (RSA). For the geometric ornaments analytical expressions for entropy and complexity measures are presented, while
for the RSA patterns these are calculated numerically. We compare the information-gain complexity measure with some alternative
measures and show advantages of the former one, as applied to two-dimensional structures. Namely, this does not require knowledge
of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.
Received 12 November 1999 相似文献
3.
Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities 总被引:2,自引:0,他引:2 下载免费PDF全文
We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network (UPTN) in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc. 相似文献
4.
Y. Zimmels 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(2):205-215
The partitioning, uniqueness and form of field energy stored in matter, and its properties as a state function, is established.
Consequently, the first and second laws apply to the nonfield and field parts of the internal energy as separate entities.
This provides a bridge between thermodynamics and the classical theory of electromagnetism. Presentation of the temperature
as the sum of nonfield and field contributions is used to establish field dependent barriers to temperature decrease toward
the absolute zero, and the existence of field induced temperature jumps. These temperature jumps appear at the instant the
field is switched on, or turned off. The partitioning of field and nonfield energies is illustrated for a specific case of
an ideal gas, and the heat absorbed by the field is derived in terms of difference in adiabatic magnetization. Finally, the
current, restrictive, form of electromagnetic field energy density is redefined with respect to the effect of field energy
stored outside the system boundaries.
Received 6 June 2000 / Received in final form 26 March 2002 Published online 24 September 2002
RID="a"
ID="a"e-mail: zimmels@tx.technion.ac.il 相似文献
5.
K. Hikami Y. Komori 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):583-588
Studied is the elliptic Ruijsenaars model, which is a difference analogue of the Calogero-Sutherland-Moser model. Using a
novel relationship between the elliptic Ruijsenaars operator and the transfer matrix of the Belavin model, we diagonalize
the Ruijsenaars operator by the algebraic Bethe ansatz method.
Received: 29 January 1998 / Accepted: 17 April 1998 相似文献
6.
T. D. Kieu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,39(1):115-128
We introduce a class of quantum heat engines which consists of
two-energy-eigenstate systems, the simplest of quantum mechanical
systems, undergoing quantum adiabatic processes and energy exchanges
with heat baths, respectively, at different stages of a cycle. Armed
with this class of heat engines and some interpretation of heat
transferred and work performed at the quantum level, we are able to
clarify some important aspects of the second law of thermodynamics.
In particular, it is not sufficient to have the heat source hotter
than the sink, but there must be a minimum temperature difference
between the hotter source and the cooler sink before any work can be
extracted through the engines. The size of this minimum temperature
difference is dictated by that of the energy gaps of the quantum
engines involved. Our new quantum heat engines also offer a
practical way, as an alternative to Szilard's engine, to physically
realise Maxwell's daemon. Inspired and motivated by the Rabi
oscillations, we further introduce some modifications to the quantum
heat engines with single-mode cavities in order to, while respecting
the second law, extract more work from the heat baths than is
otherwise possible in thermal equilibria. Some of the results above
are also generalisable to quantum heat engines of an infinite number
of energy levels including 1-D simple harmonic oscillators and 1-D
infinite square wells, or even special cases of continuous spectra. 相似文献
7.
O.V. Kirillova 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(4):583-588
In this paper, results of investigations of the simplest mechanisms of a structure formation are presented. In frameworks
of the suggested model the main attention was focused on such characteristics as wiring of the system, clusters formation,
dynamics of the wiring. The idea to take into account an influence of the environment factor is employed in the proposed model.
Investigations of systems with such principle of a structure formation reveal that the system's dynamics has typical features
of self-organized criticality phenomenon. In the avalanche-like processes, which occur in the wiring dynamics, a power law
was found with the index close to 1.4. It is independent on the environment factor (which in a sense can be considered as
system parameter). The system wiring is approximated pretty well by the Gaussian distribution. The size of the system does
not play any role in the dynamics of the model.
Received 10 March 1999 and Received in final form 24 May 1999 相似文献
8.
V. Parfait-Pignol G. Le Caër R. Delannay 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(4):499-511
The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure
and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological
properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated.
The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire
law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally
compared with the predictions of various literature models.
Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998 相似文献
9.
We discuss the structure and the interaction of telechelic brushes. We show that the association of functionalized chain ends
is capable of giving rise to attractive interactions between telechelic brush-covered surfaces, in contrast to conventional
repulsion. Our predictions for the interaction free energy are in agreement with experimental data.
Received 12 June 2000 and Received in final form 29 January 2001 相似文献
10.
B. Leblanc E. Lutton F. Axel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(4):619-628
We present the first application of Genetic Algorithms to the analysis of data from an aperiodically ordered system, high
resolution X-Ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme.
This method paves the way to the solution of the “inverse problem”, that is the retrieval of the generating disorder from
the investigation of the spectra of an unknown sample having non crystallographic, non quasi-crystallographic order.
Received 18 March 2002 / Received in final form 3 July 2002 Published online 31 October 2002
RID="a"
ID="a"e-mail: Evelyne.Lutton@inria.fr
RID="b"
ID="b"CNRS UMR 8502 相似文献
11.
M. Ahr M. Biehl R. Urbanczik 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(3):583-588
Equilibrium states of large layered neural networks with differentiable activation function and a single, linear output unit
are investigated using the replica formalism. The quenched free energy of a student network with a very large number of hidden
units learning a rule of perfectly matching complexity is calculated analytically. The system undergoes a first order phase
transition from unspecialized to specialized student configurations at a critical size of the training set. Computer simulations
of learning by stochastic gradient descent from a fixed training set demonstrate that the equilibrium results describe quantitatively
the plateau states which occur in practical training procedures at sufficiently small but finite learning rates.
Received 16 December 1998 相似文献
12.
R. Niven H. Suyari 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,61(1):75-82
Using a q-analog of Boltzmann's combinatorial basis of entropy, the
non-asymptotic non-degenerate and degenerate combinatorial forms of the
Tsallis entropy function are derived. The new measures – supersets of the
Tsallis entropy and the non-asymptotic variant of the Shannon entropy – are
functions of the probability and degeneracy of each state, the Tsallis
parameter q and the number of entities N. The analysis extends the Tsallis
entropy concept to systems of small numbers of entities, with implications
for the permissible range of q and the role of degeneracy. 相似文献
13.
L. G. Moyano A. P. Majtey C. Tsallis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):493-500
We introduce, and numerically study, a system of N symplectically and globally coupled
standard maps localized in a d=1 lattice array. The global coupling is modulated
through a factor r-α, being
r the distance between maps. Thus, interactions are long-range (nonintegrable) when
0≤α≤1, and short-range (integrable) when α>1.
We verify that the largest Lyapunov exponent λM scales as λM ∝
N-κ(α), where κ(α) is positive when interactions are
long-range, yielding weak chaos in the thermodynamic
limit N↦∞ (hence λM→0). In the short-range case,
κ(α) appears to vanish,
and the behaviour corresponds to strong chaos. We show that, for certain
values of the control parameters of the system, long-lasting metastable states
can be present. Their duration tc scales as tc ∝Nβ(α),
where β(α) appears to be numerically in agreement with the following
behavior: β>0 for 0 ≤α< 1, and zero for α≥1.
These results are consistent with features typically found in nonextensive statistical mechanics.
Moreover, they exhibit strong similarity between the present
discrete-time system, and the α-XY Hamiltonian ferromagnetic model. 相似文献
14.
A. Chakraborti B.K. Chakrabarti 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(1):167-170
We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents
is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to
energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or
equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the
usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest,
the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering
properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the
marginal saving propensity of the agents.
Received 2 May 2000 相似文献
15.
P. Narayana Swamy 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):291-294
This is a study of q-Fermions resulting from q-deformed
algebra of harmonic oscillators arising from two distinct algebras.
Employing the first algebra, the Fock states
are constructed for the generalized Fermions obeying Pauli
exclusion principle. The distribution function and other
thermodynamic properties such as the internal energy and entropy are
derived. Another generalization of fermions from a different
q-deformed algebra is investigated which deals with q-fermions not
obeying the exclusion principle. Fock states are constructed for
this system. The basic numbers appropriate for this system are
determined as a direct consequence of the algebra. We also
establish the Jackson Derivative, which is required for the
q-calculus needed to describe these generalized Fermions. 相似文献
16.
M. Schaller K. Svozil 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,69(2):297-311
Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled
primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one
utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, “solve” the halting
problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations.
On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one
shows indeterministic behavior, whereas the second one halts. Both models are capable of challenging our understanding of
computability, causality, and space-time. 相似文献
17.
A. Dragulescu V.M. Yakovenko 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,17(4):723-729
In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of
money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount
of money per economic agent. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic
models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit.
We also discuss the role of debt, and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not
hold. The instantaneous distribution of money among the agents of a system should not be confused with the distribution of
wealth. The latter also includes material wealth, which is not conserved, and thus may have a different (e.g. power-law) distribution.
Received 22 June 2000 相似文献
18.
M. Castelnovo P. Sens J.-F. Joanny 《The European physical journal. E, Soft matter》2000,1(2-3):115-125
We investigate the equilibrium charge distribution along a single annealed polyelectrolyte chain under different conditions.
The coupling between the conformation of the chain and the local charge distribution is described for various solvent qualities
and salt concentration. In salt free solution, we find a slight charge depletion in the central part of the chain: the charges
accumulate at the ends. The effect is less important if salt is added to the solution since the charge inhomogeneity is localized
close to the chain ends over a distance of order of the Debye length. In the case of poor solvent conditions we find a different
charge per monomer in the beads and in the strings in the framework of the necklace model. This inhomogeneity leads to a charge
instability and a first order transition between spherical globules and elongated chains.
Received 19 March 1999 and Received in final form 2 August 1999 相似文献
19.
S. Datta J.K. Bhattacharjee 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(2):247-248
A technique used by Edwards and Singh [8] in the study of polymers is used to provide a simple analytic procedure for calculating
the upper bound of the energies of a class of singular potentials. The accuracy of our procedure turns out to be better than
1%.
Received 29 August 2002 / Received in final form 20 November 2002 Published online 4 February 2003
RID="a"
ID="a"e-mail: sumita@bose.res.in 相似文献
20.
R. Hanel S. Thurner 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(3):327-330
We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive
at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state.
The solutions for exponential and uniform networks are exact, the analytical approximation for the scalefree case is in perfect
agreement with simulation results. We use these
solutions to provide a theoretical understanding for biodiversity loss in experimental data of foodwebs, which
is available for the three network types discussed. The model allows in principle to estimate the critical value of
species that have to be removed from the system to induce a complete diversity collapse. 相似文献