An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling

We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\$, namely the solution to the 2~dimensional~(2D) Edwards model. The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction--to--scaling exponent~$\Delta$. Writing $\langle R_N^2 \rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D, our result shows that $\Delta = 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.Comment: 17 Pages of Revtex. No figures. Submitted to J. Phys.

Differential Form of the Collision Integral for a Relativistic Plasma

The differential formulation of the Landau-Fokker-Planck collision integral is developed for the case of relativistic electromagnetic interactions.Comment: Plain TeX, 5 page

Comparison between resistive and collisionless double tearing modes for nearby resonant surfaces

The linear instability and nonlinear dynamics of collisional (resistive) and collisionless (due to electron inertia) double tearing modes (DTMs) are compared with the use of a reduced cylindrical model of a tokamak plasma. We focus on cases where two q = 2 resonant surfaces are located a small distance apart. It is found that regardless of the magnetic reconnection mechanism, resistivity or electron inertia, the fastest growing linear eigenmodes may have high poloidal mode numbers m ~ 10. The spectrum of unstable modes tends to be broader in the collisionless case. In the nonlinear regime, it is shown that in both cases fast growing high-m DTMs lead to an annular collapse involving small magnetic island structures. In addition, collisionless DTMs exhibit multiple reconnection cycles due to reversibility of collisionless reconnection and strong ExB flows. Collisionless reconnection leads to a saturated stable state, while in the collisional case resistive decay keeps the system weakly dynamic by driving it back towards the unstable equilibrium maintained by a source term.Comment: 15 pages, 9 figure

Induced Scattering and Two-Photon Absorption of Alfven Waves with Arbitrary Propagation Angles

The equation for temporary evolution of spectral energy of collisionless Alfven waves is derived in framework of weak turbulence theory. The main nonlinear processes for such conditions are induced scattering and two quantum absorption of Alfven waves by thermal ions. The equation for velocity distribution of thermal particles is derived that describes diffusion in momentum space due to this nonlinear processes. Comparison is done with the results of another authors. Results obtained are qualitatively differ from the ones obtained for the case of Alfven waves propagation along mean magnetic field.Comment: 8 page

New results for virial coefficients of hard spheres in D dimensions

We present new results for the virial coefficients B_k with k <= 10 for hard spheres in dimensions D=2,...,8.Comment: 10 pages, 5 figures, to appear in conference proceedings of STATPHYS 2004 in Pramana - Journal of Physic

Transport coefficients and ladder summation in hot gauge theories

We show how to compute transport coefficients in gauge theories by considering the expansion of the Kubo formulas in terms of ladder diagrams in the imaginary time formalism. All summations over Matsubara frequencies are performed and the analytical continuation to get the retarded correlators is done. As an illustration of the procedure, we present a derivation of the transport equation for the shear viscosity in the scalar theory. Assuming the Hard Thermal Loop approximation for the screening of distant collisions of the hard particles in the plasma, we derive a couple of integral equations for the effective vertices which, to logarithmic accuracy, are shown to be identical to the linearized Boltzmann equations previously found by Arnold, Moore and Yaffe.Comment: 34 pages, 7 figures v2. Added discussion on box topologies for the ladder rungs. Version to appear in Phys. Rev.

COMPREHENSIVE GYROKINETIC SIMULATION OF TOKAMAK TURBULENCE AT FINITE RELATIVE GYRORADIUS

OAK B202 COMPREHENSIVE GYROKINETIC SIMULATION OF TOKAMAK TURBULENCE AT FINITE RELATIVE GYRORADIUS. A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate turbulent transport in actual experimental profiles and allow direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite beta, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}*) so as to treat the profile shear stabilization effects which break gyroBohm scaling. The code operates in a cyclic flux tube limit which allows only gyroBohm scaling and a noncyclic radial annulus with physical profile variation. The later requires an adaptive source to maintain equilibrium profiles. Simple ITG simulations demonstrate the broken gyroBohm scaling depends on the actual rotational velocity shear rates competing with mode growth rates, direct comprehensive simulations of the DIII-D {rho}*-scaled L-mode experiments are presented as a quantitative test of gyrokinetics and the paradigm

Scaling of Self-Avoiding Walks in High Dimensions

We examine self-avoiding walks in dimensions 4 to 8 using high-precision Monte-Carlo simulations up to length N=16384, providing the first such results in dimensions $d > 4$ on which we concentrate our analysis. We analyse the scaling behaviour of the partition function and the statistics of nearest-neighbour contacts, as well as the average geometric size of the walks, and compare our results to $1/d$-expansions and to excellent rigorous bounds that exist. In particular, we obtain precise values for the connective constants, $\mu_5=8.838544(3)$, $\mu_6=10.878094(4)$, $\mu_7=12.902817(3)$, $\mu_8=14.919257(2)$ and give a revised estimate of $\mu_4=6.774043(5)$. All of these are by at least one order of magnitude more accurate than those previously given (from other approaches in $d>4$ and all approaches in $d=4$). Our results are consistent with most theoretical predictions, though in $d=5$ we find clear evidence of anomalous $N^{-1/2}$-corrections for the scaling of the geometric size of the walks, which we understand as a non-analytic correction to scaling of the general form $N^{(4-d)/2}$ (not present in pure Gaussian random walks).Comment: 14 pages, 2 figure

Kolmogorov-Sinai entropy in field line diffusion by anisotropic magnetic turbulence

The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations [Rev. Mod. Phys. {\bf 64}, 961 (1992)]. In particular, a slowing down logarithmic behavior versus the so-called Kubo number $R\gg 1$ ($R = (\delta B / B_0) (\xi_\| / \xi_\bot)$, where $\delta B / B_0$ is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and $\xi_\bot$ and $\xi_\|$ are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic "percolation" transport, characterized by $R\to\infty$, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics. This research article is dedicated to the memory of Professor George M. ZaslavskyComment: 15 pages, 2 figures. Accepted for publication on Plasma Physics and Controlled Fusio