Correlation Functions for an Elastic String in a Random Potential: Instanton Approach

We develop an instanton technique for calculations of correlation functions characterizing statistical behavior of the elastic string in disordered media and apply the proposed approach to correlations of string free energies corresponding to different low-lying metastable positions. We find high-energy tails of correlation functions for the case of long-range disorder (the disorder correlation length well exceeds the characteristic distance between the sequential string positions) and short-range disorder with the correlation length much smaller then the characteristic string displacements. The former case refers to energy distributions and correlations on the distances below the Larkin correlation length, while the latter describes correlations on the large spatial scales relevant for the creep dynamics.Comment: 5 pages; 1 .eps figure include

Marginal Pinning of Quenched Random Polymers

An elastic string embedded in 3D space and subject to a short-range correlated random potential exhibits marginal pinning at high temperatures, with the pinning length $L_c(T)$ becoming exponentially sensitive to temperature. Using a functional renormalization group (FRG) approach we find $L_c(T) \propto \exp[(32/\pi)(T/T_{\rm dp})^3]$, with $T_{\rm dp}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.Comment: 4 pages, RevTeX, 1 figure inserte

Velocity-force characteristics of a driven interface in a disordered medium

Using a dynamic functional renormalization group treatment of driven elastic interfaces in a disordered medium, we investigate several aspects of the creep-type motion induced by external forces below the depinning threshold $f_c$: i) We show that in the experimentally important regime of forces slightly below $f_c$ the velocity obeys an Arrhenius-type law $v\sim\exp[-U(f)/T]$ with an effective energy barrier $U(f)\propto (f_{c}-f)$ vanishing linearly when f approaches the threshold $f_c$. ii) Thermal fluctuations soften the pinning landscape at high temperatures. Determining the corresponding velocity-force characteristics at low driving forces for internal dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius type creep $v\sim \exp[-(f_c(T)/f)^{\mu}]$ involving the reduced threshold force $f_c(T)$ alone. For d=3 we obtain a similar v-f characteristic which is, however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure

Solitons in the noisy Burgers equation

We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. In the asymmetrical case the soliton scattering modes are unstable presumably toward multi soliton production and extended diffusive modes, signalling the general non-integrability of the coupled field equations. Finally, we have shown that growing steps perform anomalous random walk with dynamic exponent z=3/2 and that the nucleation of a tip is stochastically suppressed with respect to plateau formation.Comment: 11 pages Revtex file, including 15 postscript-figure

Effect of Angiogenesis-Related Cytokines on Rotator Cuff Disease: The Search for Sensitive Biomarkers of Early Tendon Degeneration

Background Hallmarks of the pathogenesis of rotator cuff disease (RCD) include an abnormal immune response, angiogenesis, and altered variables of vascularity. Degenerative changes enhance production of pro-inflammatory, anti-inflammatory, and vascular angiogenesis-related cytokines (ARC) that play a pivotal role in the immune response to arthroscopic surgery and participate in the pathogenesis of RCD. The purpose of this study was to evaluate the ARC profile, ie, interleukin (IL): IL-1β, IL-6, IL-8, IL-10, vascular endothelial growth factor (VEGF), basic fibroblast growth factor (bFGF), and angiogenin (ANG), in human peripheral blood serum and correlate this with early degenerative changes in patients with RCD. Methods Blood specimens were obtained from 200 patients with RCD and 200 patients seen in the orthopedic clinic for nonrotator cuff disorders. Angiogenesis imaging assays was performed using power Doppler ultrasound to evaluate variables of vascularity in the rotator cuff tendons. Expression of ARC was measured by commercial Bio-Plex Precision Pro Human Cytokine Assays. Results Baseline concentrations of IL-1β, IL-8, and VEGF was significantly higher in RCD patients than in controls. Significantly higher serum VEGF levels were found in 85% of patients with RCD, and correlated with advanced stage of disease (r = 0.75; P < 0.0005), average microvascular density (r = 0.68, P < 0.005), and visual analog score (r = 0.75, P < 0.0002) in RCD patients. ANG and IL-10 levels were significantly lower in RCD patients versus controls. IL-1β and ANG levels were significantly correlated with degenerative tendon grade in RCD patients. No difference in IL-6 and bFGF levels was observed between RCD patients and controls. Patients with degenerative changes had markedly lower ANG levels compared with controls. Power Doppler ultrasound showed high blood vessel density in patients with tendon rupture. Conclusion The pathogenesis of RCD is associated with an imbalance between pro-inflammatory, anti-inflammatory, and vascular ARC

Non-Linear Stochastic Equations with Calculable Steady States

We consider generalizations of the Kardar--Parisi--Zhang equation that accomodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and non-perturbative properties. In particular, we derive generalized fluctuation--dissipation conditions on the form of the (non-linear) equations for the realization of a Gaussian probability density of the fields in the steady state. For the amorphous growth of a single height field in one dimension we give a general class of equations with exactly calculable (Gaussian and more complicated) steady states. In two dimensions, we show that any anisotropic system evolves on long time and length scales either to the usual isotropic strong coupling regime or to a linear-like fixed point associated with a hidden symmetry. Similar results are derived for textural growth equations that couple the height field with additional order parameters which fluctuate on the growing surface. In this context, we propose phenomenological equations for the growth of a crystalline material, where the height field interacts with lattice distortions, and identify two special cases that obtain Gaussian steady states. In the first case compression modes influence growth and are advected by height fluctuations, while in the second case it is the density of dislocations that couples with the height.Comment: 9 pages, revtex