Depinning in a Random Medium

We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel features due to the breakdown of hyperscaling in a random system. There is a second-order transition between a localized and a delocalized phase of the polymer; we obtain analytic results on its critical pinning strength and scaling exponents. Our results are directly related to spatially inhomogeneous Kardar-Parisi-Zhang surface growth.Comment: 11 pages (latex) with one figure (now printable, no other changes

Collective Dynamics of Random Polyampholytes

We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge $q$ and with a fluctuations in this charge of the size $Q^{-1}$ and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite $q$ we then find that the scattering approaches the limit of polyelectrolyte solutions.Comment: 13 pages including 6 figures, submitted J. Chem. Phy

Directed polymers on a Cayley tree with spatially correlated disorder

In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse direction i.e. within the shell. In this paper we take the transverse distance to be the hierarchical ultrametric distance, but other possibilities are discussed. We compute the free energy for the case of quenched disorder and show that there is a fundamental difference between the case of short range spatial correlations of the disorder which behaves similarly to the non-correlated case considered previously by Derrida and Spohn and the case of long range correlations which has a totally different overlap distribution which approaches a single delta function about q=1 for large L, where L is the length of the walk. In the latter case the free energy is not extensive in L for the intermediate and also relevant range of L values, although in the true thermodynamic limit extensivity is restored. We identify a crossover temperature which grows with L, and whenever T<T_c(L) the system is always in the low temperature phase. Thus in the case of long-ranged correlation as opposed to the short-ranged case a phase transition is absent.Comment: 23 pages, 1 figure, standard latex. J. Phys. A, accepted for publicatio

Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems

We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the field theory reveals the glassy nature of the dynamics, in particular divergent barriers and barrier distributions controling the spectrum of relaxation times. A naive single relaxation time approximation for each wavevector is found to be unsatisfactory. A second approximation based on a random friction model, yields a size (L) dependent log-normal distribution of relaxation times (mean barriers ~L^\theta and variance ~ L^{\theta/2}) and a procedure to estimate dynamical scaling functions. Finally, we study the full structure of the running dynamical effective action within the field theory. We find that relaxation time distributions are non-trivial (broad but not log-normal) and encoded in a closed hierarchy of FRG equations. A thermal boundary layer ansatz (TBLA) appears as a consistent solution. It extends the one discovered in the statics which was shown to embody droplet thermal fluctuations. Although perturbative control remains a challenge, the structure of the dynamical TBLA which encodes barrier distributions opens the way for deeper understanding of the field theory approach to glasses

Analysis of the impact of climate change on groundwater related hydrological fluxes: a multi-model approach including different downscaling methods

Climate change related modifications in the spatio-temporal distribution of precipitation and evapotranspiration will have an impact on groundwater resources. This study presents a modelling approach exploiting the advantages of integrated hydrological modelling and a broad climate model basis. We applied the integrated MIKE SHE model on a perialpine, small catchment in northern Switzerland near Zurich. To examine the impact of climate change we forced the hydrological model with data from eight GCM-RCM combinations showing systematic biases which are corrected by three different statistical downscaling methods, not only for precipitation but also for the variables that govern potential evapotranspiration. The downscaling methods are evaluated in a split sample test and the sensitivity of the downscaling procedure on the hydrological fluxes is analyzed. The RCMs resulted in very different projections of potential evapotranspiration and, especially, precipitation. All three downscaling methods reduced the differences between the predictions of the RCMs and all corrected predictions showed no future groundwater stress which can be related to an expected increase in precipitation during winter. It turned out that especially the timing of the precipitation and thus recharge is very important for the future development of the groundwater levels. However, the simulation experiments revealed the weaknesses of the downscaling methods which directly influence the predicted hydrological fluxes, and thus also the predicted groundwater levels. The downscaling process is identified as an important source of uncertainty in hydrological impact studies, which has to be accounted for. Therefore it is strongly recommended to test different downscaling methods by using verification data before applying them to climate model data

Collapse or Swelling Dynamics of Homopolymer Rings: Self-consistent Hartree approach

We investigate by the use of the Martin - Siggia - Rose generating functional technique and the self - consistent Hartree approximation, the dynamics of the ring homopolymer collapse (swelling) following an instantaneous change into a poor (good) solvent conditions.The equation of motion for the time dependent monomer - to - monomer correlation function is systematically derived. It is argued that for describing of the coarse - graining process (which neglects the capillary instability and the coalescence of ``pearls'') the Rouse mode representation is very helpful, so that the resulting equations of motion can be simply solved numerically. In the case of the collapse this solution is analyzed in the framework of the hierarchically crumpled fractal picture, with crumples of successively growing scale along the chain. The presented numerical results are in line with the corresponding simple scaling argumentation which in particular shows that the characteristic collapse time of a segment of length $g$ scales as $t^* \sim \zeta_0 g/\tau$ (where $\zeta_0$ is a bare friction coefficient and $\tau$ is a depth of quench). In contrast to the collapse the globule swelling can be seen (in the case that topological effects are neglected) as a homogeneous expansion of the globule interior. The swelling of each Rouse mode as well as gyration radius $R_g$ is discussed.Comment: 20 pages, 7 figures, submitted to Phys. Rev.

The Hartree approximation in dynamics of polymeric manifolds in the melt

The Martin-Siggia-Rose (MSR) functional integral technique is applied to the dynamics of a D - dimensional manifold in a melt of similar manifolds. The integration over the collective variables of the melt can be simply implemented in the framework of the dynamical random phase approximation (RPA). The resulting effective action functional of the test manifold is treated by making use of the selfconsistent Hartree approximation. As an outcome the generalized Rouse equation (GRE) of the test manifold is derived and its static and dynamic properties are studied. It was found that the static upper critical dimension, $d_{\rm uc}=2D/(2-D)$, discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, ${\tilde d}_{uc}=2d_{\rm uc}$, distinguishes between the simple Rouse and the renormalized Rouse behavior. We have argued that the Rouse mode correlation function has a stretched exponential form. The subdiffusional exponents for this regime are calculated explicitly. The special case of linear chains, D=1, shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy

How can remote sensing contribute in groundwater modeling?

Groundwater resources assessment, modeling and management are hampered considerably by a lack of data, especially in semi-arid and arid environments with a weak observation infrastructure. Usually, only a limited number of point measurements are available, while groundwater models need spatial and temporal distributions of input and calibration data. If such data are not available, models cannot play their proper role in decision support as they are notoriously underdetermined and uncertain. Recent developments in remote sensing have opened new sources for distributed spatial data. As the relevant entities such as water fluxes, heads or transmissivities cannot be observed directly by remote sensing, ways have to be found to link the observable quantities to input data required by the model. An overview of the possibilities for employing remote-sensing observations in groundwater modeling is given, supported by examples in Botswana and China. The main possibilities are: (1) use of remote-sensing data to create some of the spatially distributed input parameter sets for a model, and (2) constraining of models during calibration by spatially distributed data derived from remote sensing. In both, models can be improved conceptually and quantitativel

Aging classification in glassy dynamics

We study the out of equilibrium dynamics of several models exhibiting aging. We attempt at identifying various types of aging systems using a phase space point of view: we introduce a trial classification, based on the overlap between two replicas of a system, which evolve together until a certain waiting time, and are then totally decoupled. We investigate in this way two types of systems, domain growth problems and spin glasses, and we show that they behave differently.Comment: 18 pages,9 Postscript figures,uses rotate.sty,epsf.st