Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise

We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by means of dynamic field theory and the renormalization group. Using a stochastic Cole--Hopf transformation we derive {\em exact} exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension $d_c = 2 (1+\rho)$. Below the lower critical dimension, there is a line $\rho_*(d)$ marking the stability boundary between the short-range and long-range noise fixed points. For $\rho \geq \rho_*(d)$, the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above $\rho_*(d)$, one has to rely on some perturbational techniques. We discuss the location of this stability boundary $\rho_* (d)$ in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure

Erratum to: Geometry effect on the estimation of band reflectance in an urban area

Reflectance of the urban surface is an important factor for urban climate studies and can be assessed using standard remote sensing applications. However, no application considers the three-dimensional structure of the city surface and its resulting shading patterns or the inclined roof surfaces. To determine the effect of these factors on the estimation of urban surface reflectance, a high-resolution raster-based city-surface model was used to estimate the spatial solar irradiance in an example city, namely Basel in Switzerland. Eight times daily for 1year, the solar irradiance was calculated using MODTRAN and the illumination geometry of the city. Subsequently, the spatial distribution of the solar irradiance, as well as the error in assumed reflectance values were analysed. The error in estimation of reflectance increased with lower solar-elevation angle, so its maxima were found in winter. Higher visibility of the assumed atmosphere also increased the estimated error due to the lower proportion of diffuse irradiance. The error decreased with coarser spatial resolution of the pixe

Geometry effect on the estimation of band reflectance in an urban area

Reflectance of the urban surface is an important factor for urban climate studies and can be assessed using standard remote sensing applications. However, no application considers the three-dimensional structure of the city surface and its resulting shading patterns or the inclined roof surfaces. To determine the effect of these factors on the estimation of urban surface reflectance, a high-resolution raster-based city-surface model was used to estimate the spatial solar irradiance in an example city, namely Basel in Switzerland. Eight times daily for 1year, the solar irradiance was calculated using MODTRAN and the illumination geometry of the city. Subsequently, the spatial distribution of the solar irradiance, as well as the error in assumed reflectance values were analysed. The error in estimation of reflectance increased with lower solar-elevation angle, so its maxima were found in winter. Higher visibility of the assumed atmosphere also increased the estimated error due to the lower proportion of diffuse irradiance. The error decreased with coarser spatial resolution of the pixe

Universality classes in anisotropic non-equilibrium growth models

We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to rich phenomena that include novel universality classes and the possibility of first-order phase transitions and multicritical behavior. These results question the presumed scaling universality in the strong-coupling rough phase, and shed further light on the connection with generalized driven diffusive systems.Comment: 4 pages, revtex, 2 figures (eps files enclosed

Are Noachian-age ridged plains (Nplr) actually early Hesperian in age

Whether or not the Nplr units in Memnonia and Argyre truly represent ridged plains volcanism of Noachian age or are simply areas of younger (Early Hesperian age) volcanism which failed to bury older craters and therefore have a greater total crater age than really applies to the ridged plains portion of those terrains is examined. The Nuekum and Hiller technique is used to determine the number of preserved crater retention surfaces in the Memnonia and Argyre regions where Scott and Tanaka show Nplr units to be common. The results for cratered terrain (Npl) in Memnonia is summarized along with those for ridged plains (Nplr) in both Memnonia and Argyre, and they are compared with similar results obtained for Tempe Terra and Lunae Plunum

Evaluation of solar cell welds by scanning acoustic microscopy

Scanning laser acoustic microscopy was used to nondestructively evaluate solar cell interconnect bonds made by resistance welding. Both copper-silver and silver-silver welds were analyzed. The bonds were produced either by a conventional parallel-gap welding technique using rectangular electrodes or new annular gap design with a circular electrode cross section. With the scanning laser acoustic microscope, it was possible to produce a real time television image which reveales the weld configuration as it relates to electrode geometry. The effect of electrode misalinement with the surface of the cell was also determined. A preliminary metallographic analysis was performed on selected welds to establish the relationship between actual size and shape of the weld area and the information available from acoustic micrographs

Mechanics of bundled semiflexible polymer networks

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly crosslinked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of non-affine bending undulations.Comment: 5 pages, 3 figures, final version as publishe

Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

Scaling function for the noisy Burgers equation in the soliton approximation

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and exhibits the correct scaling properties. The calculation presents the first step in a many body treatment of the correlations in the Burgers equation.Comment: Replacement: Several corrections, 4 pages, Revtex file, 3 figures. To appear in Europhysics Letter