Monte Carlo Investigation of Lattice Models of Polymer Collapse in Five Dimensions

Monte Carlo simulations, using the PERM algorithm, of interacting self-avoiding walks (ISAW) and interacting self-avoiding trails (ISAT) in five dimensions are presented which locate the collapse phase transition in those models. It is argued that the appearance of a transition (at least) as strong as a pseudo-first-order transition occurs in both models. The values of various theoretically conjectured dimension-dependent exponents are shown to be consistent with the data obtained. Indeed the first-order nature of the transition is even stronger in five dimensions than four. The agreement with the theory is better for ISAW than ISAT and it cannot be ruled out that ISAT have a true first-order transition in dimension five. This latter difference would be intriguing if true. On the other hand, since simulations are more difficult for ISAT than ISAW at this transition in high dimensions, any discrepancy may well be due to the inability of the simulations to reach the true asymptotic regime.Comment: LaTeX file, 16 pages incl. 7 figure

Theoretical study of space plasmas Final report, 16 Feb. 1964 - 15 Mar. 1965

Interchange stability of Van Allen belt - Effect of resonant magnetic moment violation on trapped particles - Exact solution of universal instabilit

Theoretical studies of space plasmas Summary report, 3 May 1965 - 1 May 1966

Synchrotron radiation, ionospheric currents, auroral bombardment, and plasma instabilitie

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.

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

Nonlinear structures: explosive, soliton and shock in a quantum electron-positron-ion magnetoplasma

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov-Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflect the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.Comment: 7 figure

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

Two-stream instability in finite beams

The streaming instabilities of a finite beam of charged particles passing through a zero-temperature plasma are studied. It is shown that there are no eigenmodes associated with the instabilities. Nevertheless, by constructing wave-packet disturbances one is led to instabilities similar to those for a beam of infinite extent