Parameter estimates for fractional autoregressive spatial processes

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that $\hat{d}_N-d=O_P(\frac{(\operatorname {Log}N)^3}{N})$, where $d=(d_1,d_2)$ denotes the long memory parameter.Comment: Published at http://dx.doi.org/10.1214/009053605000000589 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Heat conduction in one dimensional systems: Fourier law, chaos, and heat control

In this paper we give a brief review of the relation between microscopic dynamical properties and the Fourier law of heat conduction as well as the connection between anomalous conduction and anomalous diffusion. We then discuss the possibility to control the heat flow.Comment: 15 pages, 11 figures. To be published in the Proceedings of the NATO Advanced Research Workshop on Nonlinear Dynamics and Fundamental Interactions, Tashkent, Uzbekistan, Octo. 11-16, 200

Plasma fluctuations as Markovian noise

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.Physic

Sea-quark effects in the pion charge form factor

It is shown that the data on the pion charge form factor admit the possibility for a substantial sea-quark components in the pion wave function. If the charge form factor is calculated with instant form kinematics in a constituent quark model that is extended to include explicit $(q\bar q)^2$ components in the pion wave function, that component will give the dominant contribution to the calculated $\pi^+$ charge form factor at large values of momentum transfer. The present experimental values $Q^2$ can be described well with $(q\bar q)^2$ component admixtures of up to 50%. The sensitivity of the calculated $\pi^+$ charge form factor to whether one of the quarks or one of the antiquarks is taken to be in the P-state is small.Comment: 14 page

About a possible 3rd order phase transition at T=0 in 4D gluodynamics

We revisit the question of the convergence of lattice perturbation theory for a pure SU(3) lattice gauge theory in 4 dimensions. Using a series for the average plaquette up to order 10 in the weak coupling parameter beta^{-1}, we show that the analysis of the extrapolated ratio and the extrapolated slope suggests the possibility of a non-analytical power behavior of the form (1/\beta -1/5.7(1))^{1.0(1)}, in agreement with another analysis based on the same asumption. This would imply that the third derivative of the free energy density diverges near beta =5.7. We show that the peak in the third derivative of the free energy present on 4^4 lattices disappears if the size of the lattice is increased isotropically up to a 10^4 lattice. On the other hand, on 4 x L^3 lattices, a jump in the third derivative persists when L increases. Its location coincides with the onset of a non-zero average for the Polyakov loop. We show that the apparent contradiction at zero temperature can be resolved by moving the singularity in the complex 1/\beta plane. If the imaginary part of the location of the singularity Gamma is within the range 0.001< Gamma < 0.01, it is possible to limit the second derivative of P within an acceptable range without affecting drastically the behavior of the perturbative coefficients. We discuss the possibility of checking the existence of these complex singularities by using the strong coupling expansion or calculating the zeroes of the partition function.Comment: 7 pages, 9 figures, contains a resolution of the main paradox and a discussion of possible check

Effect of depreciation of the public goods in spatial public goods games

In this work, depreciated effect of the public goods is considered in the public goods games, which is realized by rescaling the multiplication factor r of each group as r' = r(nc/G)^beta (beat>= 0). It is assumed that each individual enjoys the full profit of the public goods if all the players of this group are cooperators, otherwise, the value of the public goods is reduced to r'. It is found that compared with the original version (beta = 0), emergence of cooperation is remarkably promoted for beta > 0, and there exit optimal values of beta inducing the best cooperation. Moreover, the optimal plat of beta broadens as r increases. Furthermore, effect of noise on the evolution of cooperation is studied, it is presented that variation of cooperator density with the noise is dependent of the value of beta and r, and cooperation dominates over most of the range of noise at an intermediate value of beta = 1.0. We study the initial distribution of the multiplication factor at beta = 1.0, and find that all the distributions can be described as Gauss distribution