Directed polymers in random media under confining force

The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx + \epsilon \Wa^\alpha, where $\eta(x,y)$ is an uncorrelated random potential and \Wa is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration $R_g(N)$ and the energy fluctuation $\Delta E(N)$ of the polymer of length $N$ in the ground state increase as $R_g(N)\sim N^{\nu}$ and $\Delta E(N)\sim N^\omega$ respectively with $\nu = 1/(1+\alpha)$ and $\omega = (1+2\alpha)/(4+4\alpha)$ for $\alpha\ge 1/2$. A novel algorithm of finding the exact ground state, with the effective time complexity of \cO(N^3), is introduced and used to confirm the conjecture numerically.Comment: 9 pages, 7 figure

Singularities of the renormalization group flow for random elastic manifolds

We consider the singularities of the zero temperature renormalization group flow for random elastic manifolds. When starting from small scales, this flow goes through two particular points $l^{*}$ and $l_{c}$, where the average value of the random squared potential turnes negative ($l^{*}$) and where the fourth derivative of the potential correlator becomes infinite at the origin ($l_{c}$). The latter point sets the scale where simple perturbation theory breaks down as a consequence of the competition between many metastable states. We show that under physically well defined circumstances $l_{c} to negative values does not take place.Comment: RevTeX, 3 page

Comment on: Role of Intermittency in Urban Development: A Model of Large-Scale City Formation

Comment to D.H. Zanette and S.C. Manrubia, Phys. Rev. Lett. 79, 523 (1997).Comment: 1 page no figure

Quantized Scaling of Growing Surfaces

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness exponent $\chi$ and the dynamic exponent $z$. Hence the exact values $\chi = 2/5, z = 8/5$ for two-dimensional and $\chi = 2/7, z = 12/7$ for three-dimensional surfaces are derived.Comment: 4 pages, revtex, no figure

Non-perturbative renormalization of the KPZ growth dynamics

We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic (self-affine) scaling are overcome with an indirect functional renormalization. The roughness exponent $\alpha$ is computed for dimensions $d=1$ to 8 and it results to be in very good agreement with the available simulations. No evidence is found for an upper critical dimension. We discuss how the present approach can be extended to other self-affine problems.Comment: 4 pages, 2 figures. To appear in Phys. Rev. Let

Controlling surface statistical properties using bias voltage: Atomic force microscopy and stochastic analysis

The effect of bias voltages on the statistical properties of rough surfaces has been studied using atomic force microscopy technique and its stochastic analysis. We have characterized the complexity of the height fluctuation of a rough surface by the stochastic parameters such as roughness exponent, level crossing, and drift and diffusion coefficients as a function of the applied bias voltage. It is shown that these statistical as well as microstructural parameters can also explain the macroscopic property of a surface. Furthermore, the tip convolution effect on the stochastic parameters has been examined.Comment: 8 pages, 11 figures

An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions.Comment: 9 pages, REVTEX, epsf, 3 postscript figures, submitted to J. Stat. Phys, a wrong character is corrected in eqs. (31) and (32

Universality and Crossover of Directed Polymers and Growing Surfaces

We study KPZ surfaces on Euclidean lattices and directed polymers on hierarchical lattices subject to different distributions of disorder, showing that universality holds, at odds with recent results on Euclidean lattices. Moreover, we find the presence of a slow (power-law) crossover toward the universal values of the exponents and verify that the exponent governing such crossover is universal too. In the limit of a 1+epsilon dimensional system we obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let

Updated Marine Mammal Distribution and Abundance Estimates in British Columbia

Information relating to the distribution and abundance of species is critical for effective conservation and management. For many species, including cetacean species of conservation concern, abundance estimates are lacking, out of date and/or highly uncertain. Systematic, line-transect marine mammal surveys were conducted in British Columbia’s (BC) coastal waters over multiple years and seasons (summer 2004, 2005, 2008, and spring/autumn 2007). In total, 10,057km of transects were surveyed in an 83,547km2 study area. Abundance estimates were calculated using two different methods: Conventional Distance Sampling (CDS) and Density Surface Modelling (DSM). CDS generates a single density estimate for each stratum, whereas DSM explicitly models spatial variation and offers potential for greater precision by incorporating environmental predictors. Although DSM yields a more relevant product for the purposes of marine spatial planning, CDS has proven to be useful in cases where there are fewer observations available for seasonal and inter-annual comparison, particularly for the scarcely observed elephant seal. The summer abundance estimates (with lower and upper 95% confidence intervals; all DSM method unless otherwise stated), assuming certain trackline detection (underestimates true population size) were: harbour porpoise (Phocoena phocoena) 8,091 (4,885–13,401); Dall’s porpoise (Phocoenoides dalli) 5,303 (4,638–6,064); Pacific white-sided dolphin (Lagenorhynchus obliquidens) 22,160 (16,522–29,721); humpback whale (Megaptera novaeangliae) 1,092 (993–1,200); fin whale (Balaenoptera physalus) 329 (274–395); killer whale (all ecotypes; Orcinus orca), 371 (222–621); common minke whale (B. acutorostrata) 522 (295–927); harbour seal (total; Phoca vitulina) 24,916 (19,666–31,569); Steller sea lion (total; Eumetopias jubatus) 4,037 (1,100–14,815); and northern elephant seal (CDS method; Mirounga angustirostris) 65 (35–121). Abundance estimates are provided on a stratum-specific basis with additional estimates provided for Steller sea lions and harbour seals that were ‘hauled out’ and ‘in water’. This analysis updates previous estimates by including additional years of effort, providing greater spatial precision with the DSM method over CDS, novel reporting for spring and autumn seasons (rather than summer alone), and providing new abundance estimates for Steller sea lion and northern elephant seal. In addition to providing a baseline of marine mammal abundance and distribution, against which future changes can be compared, this information offers the opportunity to assess the risks posed to marine mammals by existing and emerging threats, such as fisheries bycatch, ship strikes, and increased oil spill and ocean noise issues associated with increases of container ship and oil tanker traffic in British Columbia’s continental shelf waters