The dynamics of a driven interface in a disordered medium close to the depinning threshold is analyzed. By a functional renormalization group scheme exponents characterizing the depinning transition are

Abstract. The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v N ( F -F,)' for driving forces F close to its threshold value F,. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical expo- Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold F,, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For E = I the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions E = 2,3 are larger and suggest that the roughness exponent is somewhat larger than the value [ = ~/ 3 of an interface in thermal equilibrium.

We consider adsorption of random copolymer chains onto an interface within the model of Garel et al. [Europhys. Lett. 8, 9 (1989)]. By using the replica method the adsorption of the copolymer at the interface is mapped onto the problem of finding the ground state of a quantum mechanical Hamiltonian. To study this ground state we introduce a novel variational principle for the Green's function, which generalizes the well-known Rayleigh-Ritz method of quantum mechanics to nonstationary states. Minimization with an appropriate trial Green's function enables us to find the phase diagram for the localization-delocalization transition for an ideal random copolymer at the interface. [S0031-9007(98)07683-2] PACS numbers: 61.41. + eThe presence of copolymers at interfaces between two immiscible fluids is crucial to such processes as emulsion stabilization, wetting, microemulsion formation and reinforcement of polymer-polymer interfaces [1-10]. For oil-water interfaces, the polymers that are used in these applications are amphiphilic in nature. While one component is soluble in the oil phase, the other component is soluble in water. The difference in solubilities drives the copolymers to adsorb at the interface between the two phases. The localized copolymers can stabilize the interface in the sense that they significantly reduce the surface tension. The study of random copolymers has been motivated in recent years by relevance of these materials for both biological and technological applications. Moreover, the properties of these simple random systems may be important in understanding of much more complex systems such as proteins [11][12][13].It is well known that adsorption of long polymer chains on surfaces or interfaces is related to the bound-state problem of a quantum mechanical (QM) particle in a potential well [14]. The Green's function G͑r, r 0 ; s, s 0 ͒ of a chain in d spatial dimensions with the monomer s at position r and the monomer s 0 at r 0 is a fundamental quantity in the statistical mechanics of polymers. It obeys in the presence of an external potential V ͑r, s͒ the following equation:with the condition: G͑r, r 0 , 0͒ d͑r 2 r 0 ͒ and l being the statistical segment length of the polymer. Equation (1) is related to the Schrödinger equation by using the replacement: s ! it, l 2 ͑͞dkT ͒ ! 1͞m, kT !h [14,15]. Considering an external potential independent of the monomer species along the chain and given by V ͑x͒͞kT 2ud͑x͒ in one spatial dimension, a localized part of the solution exists and can be written asIt becomes the only relevant contribution for N js 2 s 0 j !`.Here the localization length j 1͞k is given by j 1͞u.However, random copolymers utilized in order to reinforce polymer-polymer interfaces do not adsorb according to the above scenario. The external potential in that case has an arc-length dependence, which in QM picture corresponds to a time dependent potential, so that an appearance of a bound state is not so obvious. In contrast to the example considered above, the individual monomers belong...

many PACS. 36.20.-r -Macromolecules and polymer molecules. PACS. 05.40-a -Fluctuation Phenomena, random processes,noise, and Brownian motion. PACS. 03.65.Fd -Algebraic methods.Abstract. -In studying the end-to-end distribution function G(r, N ) of a worm like chain by using the propagator method we have established that the combinatorial problem of counting the paths contributing to G(r, N ) can be mapped onto the problem of random walks with constraints, which is closely related to the representation theory of the Temperley-Lieb algebra. By using this mapping we derive an exact expression of the Fourier-Laplace transform of the distribution function, G(k, p), as a matrix element of an inverse of an infinite rank matrix. Using this result we also derived a recursion relation permitting to compute G(k, p) directly. We present the results of the computation of G(k, N ) and its moments. The moments < r 2n > of G(r, N ) can be calculated exactly by calculating the (1,1) matrix element of 2n-th power of a truncated matrix of rank n + 1.c EDP Sciences

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, 1/(k 2 /3 + p), through the matrix P (k, p) = (I + ikDM ) −1 D, where D and M are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-toend distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface. 61.41.+e, 82.35.Gh