Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation

Experimental realizations of a 1D interface always exhibit a finite microscopic width $\xi>0$; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface fluctuations below a characteristic temperature $T_c(\xi)$. Exploiting the exact mapping between the static 1D interface and a 1+1 Directed Polymer (DP) growing in a continuous space, we study analytically both the free-energy and geometrical fluctuations of a DP, at finite temperature $T$, with a short-range elasticity and submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi$. We derive the exact `time'-evolution equations of the disorder free-energy $\bar{F}(t,y)$, its derivative $\eta (t,y)$, and their respective two-point correlators $\bar{C}(t,y)$ and $\bar{R}(t,y)$. We compute the exact solution of its linearized evolution $\bar{R}^{lin}(t,y)$, and we combine its qualitative behavior and the asymptotic properties known for an uncorrelated disorder ($\xi=0$), to construct a `toymodel' leading to a simple description of the DP. This model is characterized by Brownian-like free-energy fluctuations, correlated at small $|y|<\xi$, of amplitude $\tilde{D}_{\infty}(T,\xi)$. We present an extended scaling analysis of the roughness predicting $\tilde{D}_{\infty} \sim 1/T$ at high-temperatures and $\tilde{D}_{\infty} \sim 1/T_c(\xi)$ at low-temperatures. We identify the connection between the temperature-induced crossover and the full replica-symmetry breaking in previous Gaussian Variational Method computations. Finally we discuss the consequences of the low-temperature regime for two experimental realizations of KPZ interfaces, namely the static and quasistatic behavior of magnetic domain walls and the high-velocity steady-state dynamics of interfaces in liquid crystals.Comment: 33 pages, 6 figures. The initial preprint arXiv:1209.0567v1 has been split into two parts upon refereeing process. The first part gathers the analytical results and is published (see reference below). It corresponds to the current version of arXiv:1209.0567. The second part gathers the numerical results and corresponds the other arXiv preprint arXiv:1305.236

Depinning of domain walls with an internal degree of freedom

Taking into account the coupling between the position of the wall and an internal degree of freedom, namely its phase $\phi$, we examine, in the rigid wall approximation, the dynamics of a magnetic domain wall subject to a weak pinning potential. We determine the corresponding force-velocity characteristics, which display several unusual features when compared to standard depinning laws. At zero temperature, there exists a bistable regime for low forces, with a logarithmic behavior close to the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different topological modes of the phase evolution. At finite temperature, the force-velocity characteristics become non-monotonous. We compare our results to recent experiments on permalloy nanowires

Sharing with Caution: Managing Parking Spaces in Vehicular Networks

By exchanging events in a vehicular ad hoc network (VANET), drivers can receive interesting information while driving. For example, they can be informed of available parking spaces in their vicinity. A suitable protocol is needed to disseminate the events efficiently within the area where they are relevant. Moreover, in such a competitive context where each vehicle may be interested in a resource, it is crucial not to communicate that resource to each driver in the vicinity. Otherwise, those drivers would waste time trying to reach a parking space and only one of them would be fulfilled, which would lead to a poor satisfaction in the system. To solve this problem, we detail in this paper a reservation protocol that efficiently allocates parking spaces in vehicular ad hoc networks and avoids the competition among the vehicles. We have integrated our protocol within VESPA, a system that we have designed for vehicles to share information in VANETs. An experimental evaluation is provided, which proves the usefulness and benefits of our reservation protocol in both parking lots and urban scenarios. Besides, we present an in-depth study of the state of the art on this topic, that shows the interest and the originality of our approach

From bulk descriptions to emergent interfaces: connecting the Ginzburg-Landau and elastic line models

Controlling interfaces is highly relevant from a technological point of view. However, their rich and complex behavior makes them very difficult to describe theoretically, and hence to predict. In this work, we establish a procedure to connect two levels of descriptions of interfaces: for a bulk description, we consider a two-dimensional Ginzburg-Landau model evolving with a Langevin equation, and boundary conditions imposing the formation of a rectilinear domain wall. At this level of description no assumptions need to be done over the interface, but analytical calculations are almost impossible to handle. On a different level of description, we consider a one-dimensional elastic line model evolving according to the Edwards-Wilkinson equation, which only allows one to study continuous and univalued interfaces, but which was up to now one of the most successful tools to treat interfaces analytically. To establish the connection between the bulk description and the interface description, we propose a simple method that applies both to clean and disordered systems. We probe the connection by numerical simulations at both levels, and our simulations, in addition to making contact with experiments, allow us to test and provide insight to develop new analytical approaches to treat interfaces