Randomly Charged Polymers, Random Walks, and Their Extremal Properties

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe

Statistical properties of charged interfaces

We consider the equilibrium statistical properties of interfaces submitted to competing interactions; a long-range repulsive Coulomb interaction inherent to the charged interface and a short-range, anisotropic, attractive one due to either elasticity or confinement. We focus on one-dimensional interfaces such as strings. Model systems considered for applications are mainly aggregates of solitons in polyacetylene and other charge density wave systems, domain lines in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature, we find a shape instability which lead, via phase transitions, to tilted phases. Depending on the regime, elastic or confinement, the order of the zero-temperature transition changes. Thermal fluctuations lead to a pure Coulomb roughening of the string, in addition to the usual one, and to the presence of angular kinks. We suggest that such instabilities might explain the tilting of stripes in cuprate oxides. The 3D problem of the charged wall is also analyzed. The latter experiences instabilities towards various tilted phases separated by a tricritical point in the elastic regime. In the confinement regime, the increase of dimensionality favors either the melting of the wall into a Wigner crystal of its constituent charges or a strongly inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure

Equilibrium shapes of flat knots

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.Comment: 4 pages, 3 figure

Tightness of slip-linked polymer chains

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops which can exchange length between each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip-links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.Comment: 10 pages, 6 figures, REVTeX

Poloidal inhomogeneity of the particle fluctuation induced fluxes near of the LCFS at lower hybrid heating and improved confinement transition at the FT-2 tokamak

This paper deals with the new spectral and microturbulence experimental data and their analysis, which show, that the radial electric field Er generated at the LH heating (LHH) in the FT-2 is high enough to form the transport barriers. The ETB is formed when LHH is switched off. The radial fluctuation-induced EB drift flux densities near LCFS in SOL are measured at two different poloidal angles. For this purpose two Langmuir probes located at low and high field sides of the torus are used. Registration of the poloidal and radial components of the electric field and density fluctuations at the same time during one discharge permits to measure the poloidal asymmetry of the transport reduction mechanism of the radial and poloidal particle fluxes in the SOL. The absolute E(~) fluctuation levels show dependence on the sign of Er shear. The modification of the microscale turbulence by the poloidal Er x B rotation shear EB at the L - H transition near LCFS is also studied by X-mode fluctuation Reflectometry. The new data were obtained by spatial spectroscopic technique.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

A multi-stage genome-wide association study of bladder cancer identifies multiple susceptibility loci.

We conducted a multi-stage, genome-wide association study of bladder cancer with a primary scan of 591,637 SNPs in 3,532 affected individuals (cases) and 5,120 controls of European descent from five studies followed by a replication strategy, which included 8,382 cases and 48,275 controls from 16 studies. In a combined analysis, we identified three new regions associated with bladder cancer on chromosomes 22q13.1, 19q12 and 2q37.1: rs1014971, (P = 8 × 10⁻¹²) maps to a non-genic region of chromosome 22q13.1, rs8102137 (P = 2 × 10⁻¹¹) on 19q12 maps to CCNE1 and rs11892031 (P = 1 × 10⁻⁷) maps to the UGT1A cluster on 2q37.1. We confirmed four previously identified genome-wide associations on chromosomes 3q28, 4p16.3, 8q24.21 and 8q24.3, validated previous candidate associations for the GSTM1 deletion (P = 4 × 10⁻¹¹) and a tag SNP for NAT2 acetylation status (P = 4 × 10⁻¹¹), and found interactions with smoking in both regions. Our findings on common variants associated with bladder cancer risk should provide new insights into the mechanisms of carcinogenesis