Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B. Harris (Phys. Rev. Lett. 63:2819 (1989)) and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 + 110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions 2<=d<=6.Comment: 4 pages, 2 figure

The lateral occipital complex subserves the perceptual persistence of motion-defined groupings.

How are the bits and pieces of retinal information assembled and integrated to form the coherent objects that we see? One long-established principle is that elements that move as a group are linked together. For instance a fragmented line-drawing of an object, placed on a background of randomly distributed short lines, can be impossible to see. But if the object moves relative to the background, its shape is instantly recognized. Even after the motion stops, the percept of the object persists briefly before it fades into the background of random lines. Where in the brain does the percept of the object persist? Using functional brain imaging, we found that such moving line-drawings activated both motion-sensitive areas (medial temporal complex, MT+) and object-sensitive areas (lateral occipital complex, LOC). However, after the motion stopped only the LOC maintained its activity while the percept endured. Evidently a percept assembled by motion-sensitive areas like MT+ can be stored, at least briefly, in the LOC

Entropy-induced separation of star polymers in porous media

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.Comment: 14 pages, 7 figure

Multifractality of Brownian motion near absorbing polymers

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties which are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorbtion at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.Comment: 18 pages, revtex, 6 ps-figure

Two-Dimensional Copolymers and Exact Conformal Multifractality

We consider in two dimensions the most general star-shaped copolymer, mixing random (RW) or self-avoiding walks (SAW) with specific interactions thereof. Its exact bulk or boundary conformal scaling dimensions in the plane are all derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers, here calculated exactly as non rational algebraic numbers. The associated multifractal function f(alpha) are found to be identical for a random walk or a SAW in 2D. These are the first examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January 199

Mini-Proceedings of the 15th meeting of the Working Group on Rad. Corrections and MC Generators for Low Energies

The mini-proceedings of the 15th Meeting of the "Working Group on Rad. Corrections and MC Generators for Low Energies" held in Mainz on April 11, 2014, are presented. These meetings, started in 2006, have as aim to bring together experimentalists and theorists working in the fields of meson transition form factors, hadronic contributions to $(g-2)_\mu$ and the effective fine structure constant, and development of Monte Carlo generators and Radiative Corrections for precision e+e- and tau physics.Comment: 21 pages, 7 contributions. Editors: S. E. Mueller and G. Venanzon

Detailed studies of non-linear magneto-optical resonances at D1 excitation of Rb-85 and Rb-87 for partially resolved hyperfine F-levels

Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. Great care was taken to obtain accurate experimental signals and avoid systematic errors. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the F_g=1 --> F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position of the transition due to the influence of the nearby F_g=2 --> F_e=2 transition, which is a dark resonance whose contrast is almost two orders of magnitude larger than the contrast of the bright resonance at the F_g=2 --> F_e=3 transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.Comment: 11 pages, 9 figure